The generator matrix
1 1 1 1 1 1 1 1 1 X 1 X 1 1 X X 0 X 1 0 X^2 X 1
0 X 0 0 0 0 0 0 X^2 X^2 X X X X X^2+X X^2+X X X^2 X^2+X X 0 X^2+X 0
0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X^2+X X^2 X 0 X X X^2 X X^2 0 X^2 X
0 0 0 X 0 0 0 X^2+X X^2 X X X^2+X X^2+X 0 X^2+X 0 X^2 X X^2 0 X^2 0 X^2+X
0 0 0 0 X 0 X X X^2+X 0 X 0 X^2 X^2+X 0 X^2 X 0 X^2+X X^2 X X^2+X X^2
0 0 0 0 0 X X X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X 0 X 0 0 X X 0
0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2
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+50x^15+182x^16+282x^17+474x^18+650x^19+1270x^20+1794x^21+2133x^22+2602x^23+2218x^24+1814x^25+1296x^26+746x^27+458x^28+198x^29+122x^30+44x^31+31x^32+8x^33+6x^34+4x^35+1x^38
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 3.89 seconds.