The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+78x^17+137x^18+168x^19+270x^20+424x^21+619x^22+688x^23+639x^24+456x^25+247x^26+184x^27+105x^28+32x^29+21x^30+16x^31+8x^32+2x^33+1x^36

The gray image is a linear code over GF(2) with n=92, k=12 and d=34.
This code was found by Heurico 1.16 in 89.7 seconds.