The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3+X^2  0  X  X  1  1  1  X  1 X^3+X^2  1  1 X^2
 0  X  0  X  0 X^3 X^2+X X^2 X^3+X^2+X X^2 X^2+X X^3+X^2 X^3+X  X  X  X X^3+X^2+X X^2 X^3+X^2+X X^3+X  0 X^2 X^2  0 X^2 X^3+X^2+X  X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^2  0  0 X^3+X^2+X X^3 X^3+X^2+X X^2+X X^3 X^3+X^2 X^3+X^2+X  X X^3+X X^3 X^3+X^2+X X^2  X X^2 X^2 X^3+X
 0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  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+154x^23+229x^24+556x^25+678x^26+958x^27+690x^28+456x^29+148x^30+134x^31+37x^32+44x^33+6x^34+2x^35+2x^36+1x^40

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 59 seconds.