The generator matrix
1 0 0 0 1 1 1 1 0 1 1 1 X X X 1 1 X X 0 1 X 1 1 X 1 0 0 X 1 1 X 0 0 1 0 1 0 X 1 1 1 0 X 1 1 1 1 1 1 1 0 X 1 1 1
0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 X X+1 1 1 X X+1 X X 0 1 1 1 0 1 X X 0 X 0 1 1 1 1 1 0 X+1 X X 0 1 0 0 0 0 X+1 X+1 1 1 0 0 0
0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 X 1 X+1 1 1 X X X 1 0 1 X+1 X X 1 0 X+1 X 0 1 0 1 1 0 1 1 0 X+1 0 X X 0 X+1 0 0 0 0 0
0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 X X+1 X 0 0 0 1 X 1 1 X+1 1 X 1 X 1 X+1 1 X+1 0 X X+1 X X+1 X 1 0 0 X+1 0 1 1 X 1 X+1 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 X 0 0 0 0 X X X 0 X X 0 X X 0 0 X 0 0 X X X X 0 0 0 0 0 X 0 0 X 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X X X X X X 0 X X 0 X 0 0 0 0 X 0 0 0 0 0 X X 0 X X X 0 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X 0 0 0 0 0 X 0 X X 0 0 X 0 X 0 X X 0 X X 0 0 0 0 0 X X 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 X X X 0 X 0 X X X X X X X X 0 0 X 0 X 0 X X 0 X X 0 0 X X X 0 X 0 X X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 X 0 X X 0 0 0 0 X 0 X X 0 0 X X 0 X 0 X 0 0 X 0 0 X 0 X X X X X X 0 0 X 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X X X 0 0 X X 0 X 0 X X X X X 0 0 X X 0 0 0 0 X X X 0 X X X X X 0 X 0 0
0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X X X 0 X 0 X 0 X X 0 0 X X X 0 X X X X 0 X X 0 0 X X 0 X X 0 X 0 X 0 X X 0 0
generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+36x^40+32x^41+129x^42+154x^43+286x^44+412x^45+524x^46+630x^47+835x^48+1028x^49+1272x^50+1502x^51+1729x^52+1988x^53+2136x^54+2422x^55+2368x^56+2344x^57+2230x^58+2110x^59+1807x^60+1588x^61+1306x^62+1026x^63+847x^64+644x^65+466x^66+290x^67+231x^68+140x^69+92x^70+50x^71+40x^72+16x^73+29x^74+8x^75+11x^76+6x^78+1x^80+2x^82
The gray image is a linear code over GF(2) with n=112, k=15 and d=40.
This code was found by Heurico 1.16 in 98.8 seconds.