The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  X  1  1  1  1  0  1  1  X  1  0  X  1  X  0
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1 X+1 X+1  X X+1 X+1  X  X  1  1  X  1  1
 0  0  1  0  0  0  0  0  0 X+1  1  X  1  0  0  X  1  1 X+1 X+1  0  0 X+1  X  X  0  0
 0  0  0  1  0  0  0  0 X+1  1  X  X  1 X+1  1  1 X+1  0  0  X  1  1  1  1  X  X  0
 0  0  0  0  1  0  0  0  1  0  1  1 X+1 X+1  X  1 X+1  1  1  X  0  1 X+1  X  X X+1  1
 0  0  0  0  0  1  0  1  0  1  0 X+1 X+1  X  X  1  1  X  X X+1 X+1  1  1  0  1  X  1
 0  0  0  0  0  0  1  1 X+1  X  1  0 X+1  X  X  1 X+1 X+1  0  X X+1 X+1  0  1  X X+1  X
 0  0  0  0  0  0  0  X  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  0  X  0  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+86x^17+222x^18+420x^19+634x^20+934x^21+1425x^22+1856x^23+2483x^24+3054x^25+3303x^26+3618x^27+3560x^28+3098x^29+2606x^30+1946x^31+1325x^32+928x^33+600x^34+338x^35+182x^36+88x^37+33x^38+14x^39+7x^40+4x^41+3x^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 32.1 seconds.