The generator matrix

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

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+14x^20+104x^21+14x^22+112x^23+1x^24+8x^25+1x^26+1x^34

The gray image is a code over GF(2) with n=176, k=8 and d=80.
This code was found by Heurico 1.16 in 0.016 seconds.