The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X+2 X^2+X+3  3 X^2+X X^2+X  0
 0  0  2  0  2  0  0  2  2  0  0  2  0
 0  0  0  2  2  2  2  2  2  0  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+21x^10+72x^11+331x^12+176x^13+329x^14+72x^15+19x^16+1x^18+1x^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.