The generator matrix

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

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+38x^23+283x^24+444x^25+1011x^26+604x^27+987x^28+408x^29+259x^30+24x^31+8x^32+12x^33+9x^34+4x^35+1x^36+1x^38+2x^39

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 0.078 seconds.