The generator matrix

 1  0  0  0  1  1  1 X^2 X^2+X  1  0  1  X  1  1  1  X  1  0  0 X^2  0  1
 0  1  0  0  0  1  1  1  1 X^2+X  1 X^2+1  0 X^2  X X^2+X  0 X^2+X+1  1  1  1  1  0
 0  0  1  0  1  1  0  1  1  0  X  X  1  1  X X+1  X X+1  X  1 X+1 X^2+1  0
 0  0  0  1  1  0  1 X+1  X X+1  1  X  1  0 X^2  0  1 X^2+X+1 X+1 X^2 X^2+X+1 X+1  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 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+66x^16+266x^17+610x^18+1482x^19+2339x^20+4078x^21+4606x^22+5742x^23+4758x^24+4118x^25+2370x^26+1462x^27+508x^28+242x^29+90x^30+18x^31+7x^32+4x^34+1x^36

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 8.06 seconds.