The generator matrix

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

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+24x^24+164x^25+277x^26+162x^27+241x^28+80x^29+24x^30+42x^31+5x^32+2x^34+1x^38+1x^40

The gray image is a linear code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 0.125 seconds.