The generator matrix

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

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+50x^17+614x^18+1380x^19+3687x^20+6186x^21+8804x^22+6448x^23+3717x^24+1182x^25+558x^26+108x^27+17x^28+6x^29+8x^30+2x^32

The gray image is a linear code over GF(2) with n=176, k=15 and d=68.
This code was found by Heurico 1.16 in 3.05 seconds.