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.