The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+94x^8+32x^9+212x^10+128x^11+40x^12+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 3.81e-009 seconds.