The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+177x^38+822x^39+1455x^40+1944x^41+2365x^42+2830x^43+2690x^44+2008x^45+1010x^46+604x^47+331x^48+92x^49+21x^50+12x^51+10x^52+4x^53+3x^54+2x^55+1x^56+2x^59

The gray image is a code over GF(2) with n=344, k=14 and d=152.
This code was found by Heurico 1.16 in 1.58 seconds.