The generator matrix

 1  0  1  1  1  2 X^2+X  1  1 X^2+X+2  1  1  1  1  1  1  1  1  1  1 X^2  0
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+X  1  3 X^2+X+1 X^2+3  1 X+1 X+1 X+3 X^2  0 X^2+X+1  1  1
 0  0 X^2 X^2+2  2 X^2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2+2  0  2 X^2+2 X^2 X^2+2 X^2 X^2 X^2+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+219x^20+128x^21+336x^22+128x^23+205x^24+5x^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 6.87e-008 seconds.