The generator matrix

 1  0  0  0  1  1  1 X^2+X  1 X^3  1 X^3+X^2  1  1  0  1 X^3+X^2  1  1  1 X^3+X^2+X  1
 0  1  0  0  X X^3+1 X^3+1  1 X^2 X^2+X X^3+X^2+X+1  1  0 X^3+X+1 X^3 X^3+X+1 X^2+X X^2 X^3+X^2+X+1 X^3+X^2+X  1 X^3
 0  0  1  0 X+1  1  X X+1 X^2+X+1  1  0  X  X X^2+X+1 X^2 X^2+1  1 X^3+X^2+1  0 X^2+X  X  0
 0  0  0  1  1 X^2 X+1 X^2+X+1 X^2+X X^2+1  X X^2+X+1  1  X  1 X^2+X+1 X^2 X^3 X^2+X X^2+X  1  0
 0  0  0  0 X^2 X^3 X^3+X^2 X^2  0 X^2 X^2  0 X^3 X^3+X^2 X^2 X^3 X^3 X^2  0 X^2 X^2 X^3+X^2

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+145x^16+1068x^17+3655x^18+11538x^19+28133x^20+53856x^21+64568x^22+54956x^23+28392x^24+11156x^25+3375x^26+1010x^27+225x^28+48x^29+18x^30

The gray image is a linear code over GF(2) with n=176, k=18 and d=64.
This code was found by Heurico 1.16 in 123 seconds.