The generator matrix

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

generates a code of length 10 over Z4[X]/(X^3+2,2X) 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 -1.01e-007 seconds.