The generator matrix

 1  1  1  1  1  1  1  X  1  1
 0 2X  0  0  0  0  0 2X 2X  0
 0  0 2X  0  0  0 2X 2X 2X  0
 0  0  0 2X  0  0 2X  0  0 2X
 0  0  0  0 2X  0 2X  0 2X 2X
 0  0  0  0  0 2X 2X 2X  0  0

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+9x^6+16x^8+32x^9+399x^10+32x^11+12x^12+7x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=80, k=9 and d=24.
This code was found by Heurico 1.16 in 0 seconds.