The generator matrix

 1  0  0  1  1  1 X^2  1  1  1 X^2+X  1  X  X  X  X  1  1  1  1  1  1
 0  1  0  1  X X^2+X+1  1  0 X^2 X+1  1 X^2+X+1  1  0  1  1  1 X^2  1  X X^2  0
 0  0  1  1  1  0 X+1  X X+1 X^2+X+1  0  X  1  1  0  X  X X^2+X  X  0 X^2  0
 0  0  0  X  0 X^2+X  X X^2+X X^2+X X^2  0 X^2 X^2 X^2+X X^2+X  0  0 X^2  0  X  X X^2
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  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+71x^16+164x^17+332x^18+522x^19+971x^20+1384x^21+1372x^22+1294x^23+928x^24+612x^25+340x^26+102x^27+76x^28+16x^29+4x^30+2x^31+1x^36

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 0.666 seconds.