The generator matrix

1 0 0 0 0 0 0 1 1 1 0 1 1 X 1 0 1 1 X 0 X 1 X X 1 1
0 1 0 0 0 0 0 0 0 0 0 1 X+1 1 X 1 X X+1 1 X X X+1 X 0 0 0
0 0 1 0 0 0 0 0 1 1 X 0 X+1 1 X+1 X 0 X X+1 X X 0 1 0 0 0
0 0 0 1 0 0 0 1 0 X 1 X+1 X X X+1 1 1 0 X X X X+1 X+1 1 0 0
0 0 0 0 1 0 0 1 X X+1 X X+1 X 1 1 X+1 0 0 0 0 1 0 1 1 X+1 0
0 0 0 0 0 1 0 1 X+1 0 1 X 0 1 1 X+1 0 X X 1 X+1 1 1 X+1 0 0
0 0 0 0 0 0 1 X 1 X 1 X+1 0 X+1 X 0 1 X+1 1 1 X 0 1 0 1 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+27x^16+126x^17+230x^18+346x^19+519x^20+736x^21+901x^22+1166x^23+1526x^24+1666x^25+1788x^26+1758x^27+1478x^28+1238x^29+1002x^30+726x^31+490x^32+312x^33+166x^34+96x^35+51x^36+18x^37+9x^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 1.10 in 2.59 seconds.