The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+20x^7+130x^8+96x^9+512x^10+136x^11+120x^12+4x^15+5x^16

The gray image is a code over GF(2) with n=80, k=10 and d=28.
This code was found by Heurico 1.16 in 0.031 seconds.