The generator matrix

 1  0  1  1  1 X+2  1  1 3X+2  1  1  1  1
 0  1 X+1 X+2 2X+3  1  2 2X+3  1 3X+2 2X X+2 2X
 0  0 2X+2  0  0 2X 2X  2  2 2X+2  2 2X+2 2X
 0  0  0  2 2X 2X+2 2X  2 2X+2 2X+2  0 2X  2

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+122x^10+256x^11+974x^12+1408x^13+964x^14+256x^15+95x^16+18x^18+2x^20

The gray image is a code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 102 seconds.