The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  X  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  0  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  0  X  X  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+85x^12+78x^14+379x^16+297x^18+845x^20+1089x^22+2048x^23+1417x^24+4096x^25+1241x^26+2048x^27+935x^28+949x^30+376x^32+371x^34+55x^36+59x^38+3x^40+11x^42+1x^46

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 3.58 seconds.