The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+484x^40+656x^41+780x^42+724x^43+520x^44+324x^45+300x^46+124x^47+120x^48+28x^49+32x^50+2x^52+1x^56

The gray image is a code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.16 in 0.125 seconds.