The generator matrix

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

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+167x^16+32x^17+518x^18+288x^19+1418x^20+704x^21+1918x^22+704x^23+1465x^24+288x^25+498x^26+32x^27+142x^28+10x^30+6x^32+1x^40

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 14.4 seconds.