The generator matrix

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

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+214x^40+396x^41+315x^42+354x^43+259x^44+224x^45+163x^46+74x^47+21x^48+8x^49+17x^50+1x^56+1x^58

The gray image is a code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 0.063 seconds.