The generator matrix
1 1 1 1 1 1 X 0 1 1 1 1 1
0 X 0 X+2 2 3X+2 X+2 X 2X+2 3X+2 X X 0
0 0 2X+2 0 2 2 2X 2X 0 2X+2 2 2 0
0 0 0 2X 2X 0 0 2X 0 2X 0 2X 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+51x^10+42x^11+270x^12+304x^13+267x^14+36x^15+47x^16+1x^18+2x^19+2x^20+1x^22
The gray image is a code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.