The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0  0  2  2
 0  0  2  0  0  2  0  2  2  0
 0  0  0  2  0  2  2  2  0  0
 0  0  0  0  2  2  2  0  0  2

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+15x^8+224x^10+15x^12+1x^20

The gray image is a code over GF(2) with n=80, k=8 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.