The generator matrix

1 0 0 0 0 1 1 1 X 1 1 1 1 0 1 0 0 1 X 1 X 0 X 1 0 1 1 X 1 1 1 0 0 X 1 0 1
0 1 0 0 0 0 0 0 0 0 0 X X 1 X+1 1 1 X+1 1 1 X 1 1 X 0 X 0 1 X X+1 X+1 X 1 1 X+1 X 0
0 0 1 0 0 0 1 1 1 0 X 1 X+1 1 1 X 1 0 X X+1 1 X+1 X 1 X 0 1 1 X+1 X 0 X 0 0 X+1 1 X
0 0 0 1 0 1 0 X+1 1 1 X 1 X X X+1 0 X+1 0 X+1 X 0 0 1 1 1 X 0 0 1 0 X 1 X 0 1 X+1 0
0 0 0 0 1 1 X+1 X 1 X 1 X+1 X 1 0 X+1 1 0 0 X+1 1 1 1 X 1 1 1 X 0 0 X 0 0 X 1 1 X+1
0 0 0 0 0 X X 0 0 0 0 0 0 0 0 0 X X X 0 X X X X X X 0 0 0 X 0 X X X 0 0 0

generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+71x^30+128x^31+137x^32+166x^33+171x^34+158x^35+163x^36+168x^37+133x^38+138x^39+135x^40+128x^41+105x^42+82x^43+73x^44+48x^45+32x^46+6x^47+3x^48+2x^49

The gray image is a linear code over GF(2) with n=74, k=11 and d=30.
This code was found by Heurico 1.10 in 0.093 seconds.