The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+34x^25+175x^26+356x^27+584x^28+818x^29+1272x^30+1718x^31+2483x^32+3016x^33+3791x^34+4550x^35+5043x^36+5678x^37+5823x^38+6044x^39+5368x^40+4686x^41+3913x^42+3132x^43+2338x^44+1610x^45+1234x^46+762x^47+524x^48+264x^49+161x^50+74x^51+43x^52+22x^53+15x^54+4x^55

The gray image is a linear code over GF(2) with n=76, k=16 and d=25.
This code was found by Heurico 1.11 in 106 seconds.