The generator matrix

 1  0  0  1  1  1 X^3+X X^3+X^2+X X^3  1  1  1  1  X X^3+X^2  1  0  1 X^2  1  X  1
 0  1  0 X^2 X^2+1  1  1  1 X^3+X^2+X X^3+X^2 X^2+X+1 X^3+1 X^3+X  1  1 X+1  1 X^3+X^2+X  1 X^3+X+1  1 X^3
 0  0  1 X^2+X+1 X+1 X^2 X^2+1 X^3+X+1  1 X^2+X  X X^3+1 X^2+1  X X^3+X^2+1  1 X^3+X^2+X  X X+1 X^3 X^3+X^2 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+132x^19+682x^20+768x^21+1182x^22+488x^23+579x^24+196x^25+42x^26+12x^27+10x^28+4x^29

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 0.047 seconds.