The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+135x^8+752x^10+135x^12+1x^20

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 1.05e-007 seconds.