The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+266x^18+320x^19+681x^20+472x^21+728x^22+440x^23+575x^24+264x^25+282x^26+40x^27+23x^28+4x^30

The gray image is a linear code over GF(2) with n=88, k=12 and d=36.
This code was found by Heurico 1.16 in 0.881 seconds.