The generator matrix

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

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+123x^16+130x^17+425x^18+540x^19+1006x^20+1258x^21+1923x^22+2490x^23+2944x^24+3732x^25+3478x^26+3768x^27+3048x^28+2596x^29+1919x^30+1268x^31+970x^32+458x^33+425x^34+124x^35+98x^36+18x^37+21x^38+2x^39+2x^40+1x^46

The gray image is a linear code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.16 in 26.5 seconds.