The generator matrix

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

generates a code of length 25 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+44x^15+195x^16+362x^17+542x^18+912x^19+1328x^20+1866x^21+2514x^22+3136x^23+3609x^24+3676x^25+3604x^26+3176x^27+2512x^28+1996x^29+1388x^30+852x^31+512x^32+282x^33+142x^34+72x^35+32x^36+10x^37+2x^38+3x^40

The gray image is a linear code over GF(2) with n=50, k=15 and d=15.
This code was found by Heurico 1.16 in 25.9 seconds.