The generator matrix
1 0 1 1 1 1 1 1 1 0
0 1 X+1 0 X+1 2X+3 0 3X+2 X+1 1
0 0 2 0 0 2X 2 2 2X+2 2X
0 0 0 2X+2 2X 2 2X+2 2X 2 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+48x^7+322x^8+720x^9+1920x^10+720x^11+312x^12+48x^13+5x^16
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 11.4 seconds.