The generator matrix

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

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+65x^20+76x^21+122x^22+156x^23+159x^24+184x^25+172x^26+200x^27+165x^28+188x^29+163x^30+140x^31+108x^32+64x^33+47x^34+16x^35+14x^36+7x^38+1x^42

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 0.153 seconds.