The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0  1 X^2  1  X X^2  X  0 X^2
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+1  1 X^2+X X^2 X+1  1 X^2+X+1  1  0  1  1 X^2  X  1
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0  X  0  0  X  X X^2  X  X  X  0  X
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  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+69x^16+52x^17+173x^18+316x^19+593x^20+964x^21+1216x^22+1420x^23+1210x^24+988x^25+602x^26+308x^27+158x^28+44x^29+56x^30+4x^31+16x^32+1x^34+1x^36

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 0.722 seconds.