The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1 X^2+X  1  1 X^3+X  1  1 X^3  1  1  1  1  X X^3+X^2+X X^3  0  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2 X^2+X+1  1 X^3+X  1  1 X^3 X+1  1 X^3+X^2+X X^2+1  1 X^2  X X^2 X^3+1 X^3+X^2+X  1  1 X^2 X+1
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^2  0 X^2 X^3  0 X^2 X^3 X^2 X^2 X^2 X^3+X^2  0 X^2 X^2 X^2 X^3  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+102x^23+237x^24+714x^25+382x^26+1212x^27+491x^28+684x^29+124x^30+86x^31+34x^32+10x^33+6x^34+8x^35+5x^36

The gray image is a linear code over GF(2) with n=216, k=12 and d=92.
This code was found by Heurico 1.16 in 3.3 seconds.