The generator matrix

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

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+18x^8+168x^9+156x^10+144x^11+12x^12+8x^13+4x^14+1x^16

The gray image is a code over GF(2) with n=80, k=9 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.