The generator matrix

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

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+203x^16+682x^17+1525x^18+2318x^19+3879x^20+4868x^21+5522x^22+5070x^23+4230x^24+2330x^25+1329x^26+530x^27+167x^28+72x^29+40x^30+2x^31

The gray image is a linear code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.13 in 3.09 seconds.