The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  1  1  1  0  X  0  0  0
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0  0 X+1 X+1  1 X+1 X+1  0  0  1  0  X  1  1
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  X  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  0  0  X  0  X  X  0
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  X  0  X  X  X  X  X  0  0  0  X  0  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  X  0  0  X  0  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  X  X  0  X  0  0  0  X  0  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+29x^20+32x^21+65x^22+64x^23+80x^24+96x^25+100x^26+128x^27+78x^28+96x^29+62x^30+64x^31+55x^32+32x^33+20x^34+13x^36+9x^38

The gray image is a linear code over GF(2) with n=54, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0485 seconds.