The generator matrix

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

generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+124x^25+259x^26+478x^27+855x^28+1170x^29+1597x^30+2212x^31+3086x^32+3910x^33+4519x^34+5310x^35+5916x^36+6276x^37+6133x^38+5316x^39+4742x^40+4020x^41+3109x^42+2358x^43+1523x^44+1014x^45+699x^46+424x^47+251x^48+122x^49+65x^50+30x^51+10x^52+4x^53+3x^54

The gray image is a linear code over GF(2) with n=74, k=16 and d=25.
This code was found by Heurico 1.11 in 104 seconds.