The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  X  X X^2+2  X
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X X^2+X X^2+X+2  X X^2+X+2  X  X X+2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X+2 X^2+X X^2+2  X X+2 X^2+2 X^2+2 X^2+X X^2+X+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+330x^20+384x^22+294x^24+14x^28+1x^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 0.031 seconds.