The generator matrix
1 0 1 1 1 3X 1 X 2X+2 1
0 1 1 2 3X+1 1 3X+2 X+2 1 2
0 0 X 3X+2 2X+2 3X+2 0 X X X+2
0 0 0 2X 0 0 2X 2X 2X 0
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+74x^7+305x^8+794x^9+1764x^10+786x^11+286x^12+70x^13+12x^14+4x^15
The gray image is a code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.015 seconds.