The generator matrix
1 0 0 1 1 1 3X 1 1 X+2 1 1 1
0 1 0 2 1 3X+1 1 2 3X 1 X+2 2X+1 X+2
0 0 1 X+3 1 2 3 X X+2 0 2X X+1 3
0 0 0 2X 2X 2X 0 0 0 2X 2X 0 0
generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+163x^10+864x^11+1476x^12+3218x^13+1458x^14+830x^15+155x^16+14x^17+11x^18+2x^19
The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.094 seconds.