The generator matrix

 1  0  1  1  1 2X  1  1  1  1
 0  1 X+1 X+2  3  1 2X+2 2X 3X  2
 0  0  2  0 2X 2X+2 2X 2X+2  0  2
 0  0  0 2X 2X 2X  0  0  0 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+192x^8+384x^9+904x^10+384x^11+172x^12+8x^14+3x^16

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.219 seconds.