The generator matrix

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

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+115x^10+384x^11+778x^12+1552x^13+794x^14+352x^15+91x^16+16x^17+11x^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 0.031 seconds.