The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+138x^17+1050x^18+3002x^19+7329x^20+12782x^21+17000x^22+12686x^23+7409x^24+2950x^25+988x^26+182x^27+11x^28+2x^29+2x^31+2x^32+2x^34

The gray image is a linear code over GF(2) with n=176, k=16 and d=68.
This code was found by Heurico 1.16 in 11.9 seconds.