The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^7+194x^8+412x^9+772x^10+408x^11+172x^12+36x^13+12x^14+2x^15+1x^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 0.016 seconds.