The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+96x^37+551x^38+1408x^39+2766x^40+3982x^41+4634x^42+5526x^43+5506x^44+3912x^45+2321x^46+1246x^47+509x^48+182x^49+77x^50+26x^51+18x^52+4x^53+2x^55+1x^58

The gray image is a code over GF(2) with n=344, k=15 and d=148.
This code was found by Heurico 1.16 in 5.72 seconds.