The generator matrix

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

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+72x^18+160x^19+420x^20+592x^21+1051x^22+1024x^23+1514x^24+1072x^25+1098x^26+592x^27+362x^28+128x^29+76x^30+16x^31+5x^32+6x^34+2x^36+1x^38

The gray image is a linear code over GF(2) with n=96, k=13 and d=36.
This code was found by Heurico 1.16 in 0.673 seconds.