The generator matrix

 1  1  1  1  1  1  1  1  2  2
 0  X  0 X+2  2 2X+2 3X+2  X 2X+2 2X+2
 0  0 2X+2  0  2 2X  2  2  0 2X
 0  0  0 2X 2X 2X  0 2X  0  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+226x^8+576x^10+216x^12+5x^16

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.