The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+72x^31+174x^32+126x^33+82x^34+152x^35+254x^36+188x^37+64x^38+160x^39+196x^40+144x^41+80x^42+88x^43+122x^44+52x^45+24x^46+40x^47+21x^48+2x^49+6x^50

The gray image is a linear code over GF(2) with n=76, k=11 and d=31.
This code was found by Heurico 1.16 in 31.9 seconds.