The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+41x^16+112x^17+240x^18+312x^19+535x^20+734x^21+916x^22+1208x^23+1422x^24+1788x^25+1764x^26+1540x^27+1594x^28+1400x^29+972x^30+692x^31+436x^32+308x^33+188x^34+84x^35+63x^36+10x^37+16x^38+4x^39+4x^40

The gray image is a linear code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 13.2 seconds.