The generator matrix

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

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+442x^17+1966x^18+5762x^19+15247x^20+24720x^21+34202x^22+25680x^23+15307x^24+5394x^25+1778x^26+458x^27+101x^28+4x^29+6x^30+4x^31

The gray image is a linear code over GF(2) with n=176, k=17 and d=68.
This code was found by Heurico 1.16 in 42.9 seconds.