The generator matrix

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

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+174x^25+348x^26+192x^27+60x^28+132x^29+100x^30+3x^32+14x^33

The gray image is a linear code over GF(2) with n=216, k=10 and d=100.
This code was found by Heurico 1.16 in 23.9 seconds.