The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+92x^19+246x^20+560x^21+272x^22+540x^23+246x^24+76x^25+8x^27+2x^28+4x^29+1x^32

The gray image is a linear code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.031 seconds.