The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1 1 X 1 1 1 X 1 X 1 1
0 X 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X X X X X^2+X X^2+X 0 0 X^2+X X^2+X
0 0 X 0 0 0 X X^2+X X^2+X X X 0 X X^2+X X X^2 0 X^2+X 0 X^2+X X X^2 X^2
0 0 0 X 0 X X X^2+X 0 X^2 X X^2+X 0 X X^2 0 X^2 X^2+X X^2 X^2 X^2 X 0
0 0 0 0 X X 0 X^2+X X X^2+X X^2 X 0 X^2+X 0 X^2+X X X^2 0 X X 0 X^2+X
0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2
0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0
0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0
generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+68x^15+163x^16+246x^17+358x^18+568x^19+972x^20+1652x^21+2566x^22+3068x^23+2620x^24+1728x^25+1066x^26+596x^27+306x^28+204x^29+98x^30+48x^31+32x^32+10x^33+8x^34+4x^35+2x^36
The gray image is a linear code over GF(2) with n=92, k=14 and d=30.
This code was found by Heurico 1.16 in 5.24 seconds.