The generator matrix

 1  1  1  1  1  1  1  1  X  1
 0  X 2X+2 X+2 2X 3X+2  2 3X X+2  0

generates a code of length 10 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+20x^9+85x^10+20x^11+1x^12+1x^18

The gray image is a code over GF(2) with n=80, k=7 and d=36.
This code was found by Heurico 1.16 in 0.016 seconds.