The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X  X  1 X^2+X X^2  1  0  1 X^2  1 X^2+X  1
 0  1  0  1  0  1  1  X  1  X  1  X X+1  1  1 X^2+1  0 X^2  1 X^2  1 X+1
 0  0  1  1  1  0  1 X+1  1  X X^2+X  1  X X^2+1 X^2+X+1 X+1  1 X^2+X X^2+X  0 X^2+X+1  0
 0  0  0  X  0  0  0  0  0  0  0 X^2 X^2  X  X X^2+X  X  X X^2+X X^2 X^2+X X^2
 0  0  0  0  X  0  0  0 X^2  X  X  X  X  X  X  X X^2 X^2+X X^2 X^2+X  X X^2
 0  0  0  0  0  X X^2+X X^2+X  0  X X^2+X X^2+X X^2  X X^2 X^2 X^2+X  0 X^2  0  0 X^2

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+66x^15+290x^16+562x^17+1303x^18+2330x^19+3773x^20+5156x^21+5643x^22+5322x^23+3841x^24+2404x^25+1221x^26+470x^27+279x^28+68x^29+25x^30+4x^31+8x^32+2x^33

The gray image is a linear code over GF(2) with n=88, k=15 and d=30.
This code was found by Heurico 1.16 in 8.84 seconds.