The generator matrix

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

generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+34x^9+154x^10+258x^11+933x^12+1342x^13+933x^14+252x^15+153x^16+30x^17+2x^19+1x^20+2x^21+1x^22

The gray image is a code over GF(2) with n=104, k=12 and d=36.
This code was found by Heurico 1.16 in 0.047 seconds.