The generator matrix

 1  1  1  1  1  1  1  1 2X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X 2X  0
 0  0 2X 2X 2X  0  0 2X  0  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+11x^8+124x^9+11x^10+88x^11+4x^12+12x^13+4x^14+1x^18

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 0 seconds.