The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+86x^17+220x^18+402x^19+657x^20+950x^21+1355x^22+1920x^23+2533x^24+2976x^25+3386x^26+3586x^27+3434x^28+3158x^29+2606x^30+1950x^31+1397x^32+912x^33+576x^34+324x^35+165x^36+108x^37+47x^38+10x^39+5x^40+2x^41+2x^42

The gray image is a linear code over GF(2) with n=54, k=15 and d=17.
This code was found by Heurico 1.11 in 13.1 seconds.