The generator matrix

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

generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+169x^16+72x^17+400x^18+552x^19+854x^20+1424x^21+1248x^22+1424x^23+854x^24+552x^25+400x^26+72x^27+169x^28+1x^44

The gray image is a linear code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 0.818 seconds.