The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+151x^16+180x^17+936x^18+1036x^19+2772x^20+3408x^21+5292x^22+5120x^23+5479x^24+3348x^25+2752x^26+1068x^27+868x^28+168x^29+172x^30+8x^31+8x^32+1x^40

The gray image is a linear code over GF(2) with n=92, k=15 and d=32.
This code was found by Heurico 1.16 in 9.79 seconds.