The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  X  0  X  X  0  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  1  1  1  1  1 X+1  1  X  1  1  1  1 X+1  0
 0  0  1  0  0  0  1  1  1  1  1  1  X  1  0  0  X  X  0  1 X+1 X+1  X X+1  0  1
 0  0  0  1  0  1  1  0  1  0  1  0  X X+1  1  X  0  1 X+1  X  0  1 X+1  1  X X+1
 0  0  0  0  1  1  0  1  1  0  1 X+1  0  0  X  1 X+1 X+1 X+1 X+1  1  1  0  0 X+1  X
 0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  X  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  X  0  X  X  X  0  0  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+83x^16+130x^17+446x^18+578x^19+994x^20+1376x^21+1854x^22+2480x^23+2999x^24+3508x^25+3548x^26+3684x^27+3084x^28+2704x^29+1964x^30+1312x^31+916x^32+442x^33+358x^34+138x^35+114x^36+32x^37+22x^38+1x^40

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 23.8 seconds.