The generator matrix
1 1 1 1 X 1 1 1 1 2
0 X 2X+2 X+2 X+2 0 X+2 2X+2 3X 2X+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+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 0.016 seconds.