The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 0 1 0 0 1 1 X 1 0 1 0
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 0 1 X+1 1 1 0 X+1 1 0 1 X+1 X
0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 X X X 0 0 X X X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X X X X 0 X 0 X X X 0 X
0 0 0 0 X 0 0 0 0 0 X 0 X 0 0 X X X X 0 0 X 0 X X X X
0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X 0 0 0 0 X X X X X X 0
0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X X 0 X 0 X 0 X X 0 X
0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 0 X 0 X 0 X X 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X 0 X X 0 0 X 0 0 X 0 0 X
generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+135x^20+128x^22+371x^24+352x^26+496x^28+256x^30+233x^32+32x^34+39x^36+3x^40+2x^44
The gray image is a linear code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.16 in 0.635 seconds.