The generator matrix

 1  0  0  1  1  1 X^3+X  X  1 X^3+X^2  1  1  1  1  X  1  1  1  0 X^3+X^2 X^3+X^2+X X^2+X  1  1  1  1  1
 0  1  0  0 X^3+X^2+1 X+1  1 X^3 X^2+X+1  1  X X^3+X X^2+X+1 X^3+X^2  1 X^3+X^2+1 X^2+1 X^3+X^2+X  1 X^3+X^2+X  X  1 X+1 X^3+X^2+1  0 X^3+X X^3+X^2
 0  0  1 X+1 X+1  0 X^2+X+1  1 X^2+X+1 X^2+1  1  X X^2+X X^3+X X^3+X^2  X X^3+X^2 X^3+X^2+X+1 X^2+X+1  1  1 X^2  1 X^2 X^3+X^2+X X^3+1 X^3+X+1
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^2 X^3  0  0 X^3+X^2 X^2  0  0 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2 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+372x^23+1072x^24+1994x^25+3060x^26+3252x^27+3426x^28+1942x^29+792x^30+340x^31+91x^32+30x^33+4x^34+4x^35+2x^36+2x^37

The gray image is a linear code over GF(2) with n=216, k=14 and d=92.
This code was found by Heurico 1.16 in 375 seconds.