The generator matrix

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

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+21x^8+76x^9+88x^10+40x^11+10x^12+12x^13+8x^14

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 6.87e-008 seconds.