The generator matrix

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

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+111x^16+16x^17+161x^18+80x^19+146x^20+224x^21+110x^22+432x^23+463x^24+544x^25+415x^26+432x^27+236x^28+224x^29+260x^30+80x^31+64x^32+16x^33+63x^34+2x^36+14x^38+1x^40+1x^42

The gray image is a linear code over GF(2) with n=50, k=12 and d=16.
This code was found by Heurico 1.16 in 0.523 seconds.