The generator matrix

 1  1  1  1  1  1  1  1 X^2 X^2
 0  X  0 X^2+X X^2 X^2+2 X^2+X+2  X X^2+2 X^2+2
 0  0 X^2+2  0 X^2  2 X^2 X^2  0  2
 0  0  0  2  2  2  0  2  0  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+226x^8+576x^10+216x^12+5x^16

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.031 seconds.