The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+76x^41+156x^42+112x^43+60x^44+64x^45+36x^46+2x^48+4x^49+1x^64

The gray image is a code over GF(2) with n=344, k=9 and d=164.
This code was found by Heurico 1.16 in 0.062 seconds.