The generator matrix

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

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+109x^16+16x^17+108x^18+288x^19+638x^20+1008x^21+1148x^22+1472x^23+1303x^24+1008x^25+516x^26+288x^27+224x^28+16x^29+20x^30+26x^32+2x^36+1x^40

The gray image is a linear code over GF(2) with n=92, k=13 and d=32.
This code was found by Heurico 1.16 in 0.695 seconds.