The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+X  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+2 X^2+1  1 X^2+X  2 X^2+X+2  2
 0  0 X^2  0  0  2  2 X^2+2 X^2+2 X^2 X^2+2 X^2  2
 0  0  0 X^2+2  2 X^2  2 X^2+2 X^2 X^2  0  2 X^2+2

generates a code of length 13 over Z4[X]/(X^3+2,2X) 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 99.1 seconds.