The generator matrix

 1  1  1  1  1  1  1  1  1  1 X^2  X  1
 0  X X^2+2 X^2+X  0 X^2+X  0 X^2+X  2 X^2+X+2 X^2+2 X^2+X  0
 0  0  2  0  0  2  2  2  2  0  0  0  0
 0  0  0  2  2  2  2  0  0  0  2  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+18x^10+50x^11+94x^12+190x^13+91x^14+46x^15+17x^16+2x^17+2x^18+1x^22

The gray image is a code over GF(2) with n=104, k=9 and d=40.
This code was found by Heurico 1.16 in 3.62e-008 seconds.