The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+105x^40+96x^42+640x^43+91x^44+64x^46+26x^48+1x^84

The gray image is a code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.078 seconds.