The generator matrix

 1  1  1  1  1  X  1  1  1  0  X  0  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+X X^2+2 X+2  X X+2  X  0
 0  0  2  0  0  2  0  0  2  2  0  2  0
 0  0  0  2  0  2  0  2  0  2  0  2  2
 0  0  0  0  2  2  2  2  2  2  0  0  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+40x^10+96x^11+222x^12+320x^13+208x^14+96x^15+31x^16+8x^18+2x^20

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 3.81e-009 seconds.