The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1
0 X^2+2 0 X^2 0 2 X^2+2 X^2+2 0 2 X^2+2 X^2+2 2
0 0 X^2+2 X^2 0 X^2 X^2 2 2 2 0 2 X^2
0 0 0 2 2 2 0 2 2 2 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+15x^10+42x^11+16x^12+368x^13+15x^14+36x^15+15x^16+1x^18+2x^19+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 -6.48e-008 seconds.