The generator matrix

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

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+198x^24+192x^25+436x^26+384x^27+469x^28+192x^29+156x^30+16x^32+3x^36+1x^40

The gray image is a linear code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 0.156 seconds.