The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 X X X 1 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X 0 0 X X X 0 X
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 X X X 0 X 0 X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X X X X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X 0 X 0 0 X 0 0 X 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 X X X 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X 0 X X 0 0 0 X X X X 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X X 0 0 X 0 X 0 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 0 X 0 X 0 0 X X X X X 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 X X 0 0 X X 0 0 0 0 X X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X 0 0 X X X X 0 0 X 0 X 0
generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+158x^20+371x^24+192x^26+978x^28+640x^30+1056x^32+192x^34+378x^36+105x^40+22x^44+3x^48
The gray image is a linear code over GF(2) with n=60, k=12 and d=20.
This code was found by Heurico 1.16 in 1.05 seconds.