The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+225x^20+128x^21+320x^22+128x^23+217x^24+3x^28+2x^32

The gray image is a code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.203 seconds.