The generator matrix

 1  1  1  1  1  2  1  1  1  X  1  1  1
 0  X  0 X^2+X+2 X^2  X  X X^2+2 X^2+X  2  0 X^2+X+2 X^2
 0  0 X^2+2 X^2 X^2 X^2 X^2+2  2  2 X^2+2  2  0 X^2+2

generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+46x^11+86x^12+274x^13+63x^14+18x^15+9x^16+14x^17+1x^22

The gray image is a code over GF(2) with n=104, k=9 and d=44.
This code was found by Heurico 1.16 in -3.24e-008 seconds.