The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+72x^28+52x^29+207x^30+332x^31+366x^32+422x^33+510x^34+528x^35+542x^36+690x^37+637x^38+714x^39+641x^40+630x^41+507x^42+402x^43+365x^44+226x^45+160x^46+66x^47+59x^48+28x^49+27x^50+6x^51+1x^52+1x^64

The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.10 in 1.44 seconds.