The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X 1 1 1 1 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 0 X X 0 X X X X X X 0 X 0 X X 0 X 0
0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X 0 X 0 0 0 X 0 X X 0 0 X 0 0 X 0
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X X X X 0 0 X 0 0 0 X X 0 0 0
0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 0 0 X 0 0 X X 0 X X X 0 0 0
0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X 0 X X X X 0
0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X 0 X X 0 X X X 0 X 0 0 0 X 0 0 X X X 0
0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 0 X X X X 0 0 X X X X 0 0 X X 0 X X X 0
0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 0 0 X 0 X 0 X 0 0 0 0 X X X 0 0 0 X 0
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+54x^28+30x^30+8x^31+68x^32+48x^33+62x^34+120x^35+52x^36+160x^37+52x^38+120x^39+46x^40+48x^41+60x^42+8x^43+30x^44+35x^46+5x^48+14x^50+2x^54+1x^62
The gray image is a linear code over GF(2) with n=74, k=10 and d=28.
This code was found by Heurico 1.16 in 0.109 seconds.