The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+54x^20+224x^21+86x^22+32x^23+41x^24+64x^25+9x^26+1x^34

The gray image is a linear code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 3.62e-008 seconds.