The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2 X^2+X  0 X^2  X X^2+X  X  0 X^2
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2 X^2+X X^2+X  X  X  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X  X X^2  X X^2 X^2  0
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  0 X^2 X^2+X X^2+X  X  0 X^2+X  X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0  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+123x^16+298x^18+500x^20+512x^21+1234x^22+512x^23+499x^24+302x^26+92x^28+22x^30+1x^40

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.246 seconds.