The generator matrix

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

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+64x^7+98x^8+448x^9+832x^10+448x^11+88x^12+64x^13+5x^16

The gray image is a code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.047 seconds.