The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+288x^39+846x^40+1156x^41+1382x^42+1200x^43+1440x^44+748x^45+497x^46+376x^47+145x^48+60x^49+32x^50+8x^51+8x^52+4x^53+1x^54

The gray image is a code over GF(2) with n=344, k=13 and d=156.
This code was found by Heurico 1.16 in 0.422 seconds.