The generator matrix

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

generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+164x^8+474x^9+801x^10+444x^11+139x^12+10x^13+15x^14

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.