The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+39x^20+80x^21+116x^22+162x^23+173x^24+178x^25+193x^26+190x^27+185x^28+190x^29+165x^30+142x^31+100x^32+62x^33+35x^34+18x^35+12x^36+2x^37+3x^38+2x^40

The gray image is a linear code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.16 in 0.185 seconds.