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  1  X  X  X  X  1  1  X  1  1  1  1  1  X  X  X
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  X  0  X  X  X  0  X  0  0  X  X  X  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  X  X  0  0  0  0  X  0  X  X  0  X  X  X
 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  0  X  X  X  0  X  X  X  X  0  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  0  X  X  X  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  X  0  0  X  X  X  0  X  X  0  0  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  0  X  X  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  X  0  X  0  X  0  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  0  X  0  X  0  X  0  X  0  X  0  X  0  X  0

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+64x^30+109x^32+82x^34+147x^36+226x^38+176x^40+76x^42+43x^44+60x^46+34x^48+2x^50+1x^52+2x^54+1x^60

The gray image is a linear code over GF(2) with n=76, k=10 and d=30.
This code was found by Heurico 1.16 in 29.8 seconds.