The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3+X^2  1  1  0  X  1  X  1  0  1  1 X^3+X^2  X
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X X^3+X^2+X X^3+X^2+X  X  0 X^2 X^2 X^2 X^3+X X^2+X  X X^3 X^3+X^2+X X^2  X X^3+X
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^2  X X^3+X^2 X^2 X^3+X^2+X  X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X  X X^3 X^2+X X^3+X^2+X X^2+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2  0  0 X^3+X^2  0  0 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+178x^23+232x^24+562x^25+681x^26+854x^27+666x^28+550x^29+175x^30+118x^31+27x^32+38x^33+7x^34+2x^35+2x^36+2x^37+1x^38

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 0.109 seconds.