The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 92 seconds.