The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  1  1  1  1  X  X  0  1  1  X  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  1 X+1  X  1  X  X X+1  1  1  X  0
 0  0  1  0  0  0  0  0  0 X+1  1  X  1  0  0 X+1 X+1  1  X  X  1 X+1  0 X+1  0  0
 0  0  0  1  0  0  0  0 X+1  1  X  X  1 X+1  1  X X+1  0  1  1  X  1  X  1  1  0
 0  0  0  0  1  0  0  0  1  0  1  1 X+1 X+1  X  X  0  1 X+1  0 X+1  X  1  1 X+1  0
 0  0  0  0  0  1  0  1  0  1  0 X+1 X+1  X  X X+1 X+1  0  X  1  1  X  1  1  1  0
 0  0  0  0  0  0  1  1 X+1  X  1  0 X+1  X  X  X  1  X  1  X  X  1  X  0  0  0
 0  0  0  0  0  0  0  X  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  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+151x^16+168x^17+515x^18+564x^19+1097x^20+1248x^21+1998x^22+2518x^23+2756x^24+3656x^25+3298x^26+3664x^27+2818x^28+2632x^29+2024x^30+1300x^31+1106x^32+464x^33+451x^34+140x^35+133x^36+24x^37+34x^38+6x^39+2x^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 28.8 seconds.