The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1  1  0  1  1  X  1  1  1  1 X^2+X+2 X^2 X^2+X+2  1  1 X^2+2  1  1  1 X+2  0 X^2  1 X^2  1  1  1  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+1  1  0 X^2+X+3  1 X+1 X^2+2  1 X^2+X  0 X+1 X^2+X+3  1  1  1  3 X^2+2  X  1 X^2+3  1  1  1  1 X+2  2 X^2 X^2+X+2 X^2+X+2 X^2+X+1 X+2  1  0
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2  2 X+2 X^2 X^2+2 X^2+2 X^2+X X^2+X+2 X^2+X+2 X^2+2 X^2+X  2 X+2  X X^2+2 X^2+2 X^2+X+2  0 X^2+X X^2 X^2 X^2+X+2 X^2 X^2+X+2  0 X^2  X X+2 X+2  X  0  2 X^2+X  0
 0  0  0  2  0  2  2  2  2  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  0  2  2  2  0  2  0  2  0  2  0  2  2

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+134x^39+453x^40+494x^41+817x^42+480x^43+775x^44+404x^45+273x^46+110x^47+98x^48+30x^49+4x^50+12x^51+9x^52+1x^54+1x^58

The gray image is a code over GF(2) with n=344, k=12 and d=156.
This code was found by Heurico 1.16 in 0.172 seconds.