The generator matrix

 1  0  1  1  1 3X  1  1 2X+2  1
 0  1  1  2 3X+3  1 3X+1 3X+2  1 X+2
 0  0  X 3X X+2 2X  2 2X+2 3X+2  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+164x^8+474x^9+801x^10+444x^11+139x^12+10x^13+15x^14

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.