The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2 X^2  X  X  1  X  1  X
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X  X  X X^2  X  X  0 X^2+X  X X^2
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2 X^2+X  X X^2  0  0  X X^2+X X^2  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X X^2 X^2  X  X X^2+X  0  0  0  0 X^2
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2  X X^2+X X^2 X^2+X X^2  X  X  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 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+148x^16+430x^18+64x^19+839x^20+512x^21+1616x^22+896x^23+1711x^24+512x^25+856x^26+64x^27+408x^28+104x^30+27x^32+2x^34+1x^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 1.1 seconds.