The generator matrix

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

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+230x^19+557x^20+814x^21+962x^22+812x^23+495x^24+140x^25+28x^26+46x^27+3x^28+6x^29+2x^30

The gray image is a linear code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 94.9 seconds.