The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  0  0  1  0  X  0  X  0  X  0  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  X  1  1  X  1  X  1  1  X  1  0
 0  0  1  0  0  0  0  0  0  1  1 X+1  1  1  1  1  0 X+1  1  X  0 X+1  X  X  1  0
 0  0  0  1  0  0  0  0  1  0 X+1  X X+1  0  1 X+1 X+1  X X+1  1  X  0  X X+1  X  0
 0  0  0  0  1  0  0  0  1  1  0  X  1 X+1  1  0  X  1  X  1  1 X+1  0  X  0  0
 0  0  0  0  0  1  0  1  0 X+1 X+1  X  1  1  1 X+1 X+1  0  1  0 X+1 X+1  1 X+1  X  0
 0  0  0  0  0  0  1  1 X+1  X  0 X+1  1 X+1  0  1 X+1  1  0 X+1  1 X+1  X  0  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  X  0  0  0  0  X  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+154x^17+505x^18+556x^19+1172x^20+1320x^21+1839x^22+2486x^23+2886x^24+3624x^25+3242x^26+3684x^27+2884x^28+2596x^29+1950x^30+1320x^31+1122x^32+478x^33+493x^34+144x^35+96x^36+20x^37+35x^38+2x^39+8x^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 1.11 in 11.6 seconds.