The generator matrix

 1  0  1  1  1 X^2+X  1  2  1  1  1 X^2+X+2  0
 0  1 X+1 X^2+X X^2+3  1  2  1 X^2+X+2 X+1 X^2+2  1  1
 0  0 X^2  0 X^2+2  2 X^2 X^2 X^2+2  2  0 X^2  0
 0  0  0  2  0  2  0  0  2  2  2  0  0
 0  0  0  0  2  0  2  0  0  2  2  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+107x^10+288x^11+993x^12+1344x^13+966x^14+288x^15+93x^16+15x^18+1x^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 1.81 seconds.