The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+56x^12+272x^14+210x^16+32x^17+693x^18+64x^19+448x^20+1280x^21+1912x^22+960x^23+504x^24+3520x^25+504x^26+960x^27+1912x^28+1280x^29+448x^30+64x^31+693x^32+32x^33+210x^34+272x^36+56x^38+1x^50

The gray image is a linear code over GF(2) with n=50, k=14 and d=12.
This code was found by Heurico 1.16 in 5.49 seconds.