The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1 X^2+X  0 X^2+X  0  1  0 X^2 X^2+X  1 X^2+X  1
 0  1  0  0  0  1  1  1  X X+1 X^2+1 X^2+X X^2  1  1  1  1  X  X  X X^2+X  1  0
 0  0  1  0  1  1  X X+1  0  X X+1  1 X^2 X+1  1 X^2  X  1  1  X  X X^2+1  0
 0  0  0  1  1  0 X+1  1  1 X^2  1 X^2+X  1 X^2+1  X  1 X+1  1  0  1 X^2 X^2+X+1  0
 0  0  0  0  X  0  0  0 X^2 X^2+X X^2+X  X  X X^2+X  0 X^2  X X^2+X X^2 X^2  0  X X^2
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  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+51x^16+258x^17+767x^18+1190x^19+2765x^20+3330x^21+5591x^22+4718x^23+5732x^24+3446x^25+2725x^26+1170x^27+719x^28+198x^29+69x^30+26x^31+11x^32+1x^40

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 8.57 seconds.