The generator matrix

 1  0  0  1  1  1  0 X^2  1  1 X^3+X^2+X  1  X  1  1 X^3+X  1 X^3  1  1 X^2  0  1 X^3+X  1  1  1
 0  1  0 X^2 X^2+1  1  1  X  0 X^3+X^2  1 X^3+X^2+X+1  1 X^3+X+1  X X^3 X^2+1  1 X^3+X^2+1  X  1  1 X^3+X^2+X  1  0 X^3+X^2+1  0
 0  0  1 X^2+X+1 X+1 X^2 X+1  1 X^2+X X^3+1  X X^3+X+1 X^2+X+1 X^2  1  1  X  1  1 X^2+X+1 X^2+X X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+X X^3+X^2 X^2+X+1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 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+132x^23+436x^24+1268x^25+1279x^26+2156x^27+1248x^28+986x^29+394x^30+234x^31+27x^32+18x^33+7x^34+6x^35

The gray image is a linear code over GF(2) with n=216, k=13 and d=92.
This code was found by Heurico 1.16 in 0.688 seconds.