The generator matrix

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

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+78x^17+210x^18+422x^19+656x^20+966x^21+1459x^22+1836x^23+2366x^24+3044x^25+3385x^26+3604x^27+3600x^28+3092x^29+2526x^30+2000x^31+1375x^32+910x^33+564x^34+310x^35+192x^36+102x^37+47x^38+20x^39+2x^40+1x^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 1.16 in 30 seconds.