The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  X  1  X  1  1  X  X  1  1  1  1  1
 0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0
 0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0  0  0 2X
 0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X
 0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+14x^41+11x^42+208x^43+12x^44+4x^46+3x^48+2x^57+1x^58

The gray image is a code over GF(2) with n=344, k=8 and d=164.
This code was found by Heurico 1.16 in 0.078 seconds.