The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+107x^16+154x^17+287x^18+452x^19+781x^20+968x^21+1159x^22+1484x^23+1822x^24+1944x^25+1594x^26+1716x^27+1334x^28+916x^29+706x^30+420x^31+294x^32+110x^33+87x^34+24x^35+13x^36+4x^37+7x^38

The gray image is a linear code over GF(2) with n=50, k=14 and d=16.
This code was found by Heurico 1.16 in 14.6 seconds.