The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  1
 0  X  0  X  2  0 X^2+X+2 X^2+X X^2 X^2+2 X^2+2  X  0
 0  0  X  X  0 X^2+X+2  X X^2  X X^2+X X^2+X+2  X  0
 0  0  0 X^2 X^2+2 X^2  2 X^2  0  2 X^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+42x^9+132x^10+352x^11+840x^12+1398x^13+804x^14+336x^15+135x^16+46x^17+8x^18+2x^21

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 0.031 seconds.