The generator matrix

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

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+73x^24+436x^25+295x^26+496x^27+261x^28+396x^29+53x^30+8x^31+16x^32+8x^33+3x^34+1x^36+1x^38

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 0.187 seconds.