The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X X^2  0  0 X^2  1 X^2  1  1 X^2+X  X  1
 0  1  0  1  0 X^2+X+1  1  1 X^2  X  0  1  1  1  1 X^2+X+1 X^2 X+1 X^2+1  X  0  0
 0  0  1  1  1  0  1  1  0 X^2+1  1 X^2+X+1  X X^2+X X+1  X  1  1 X^2+1  1  1  0
 0  0  0  X  0  0  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X X^2  0 X^2+X X^2  X  0  0
 0  0  0  0  X X^2+X X^2+X  0 X^2  X X^2 X^2+X X^2  X  0 X^2 X^2+X  0  X X^2+X  X  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+83x^16+222x^17+308x^18+736x^19+778x^20+1294x^21+1188x^22+1456x^23+876x^24+698x^25+284x^26+176x^27+54x^28+26x^29+12x^30

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 0.719 seconds.