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

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+34x^40+24x^42+384x^43+48x^44+8x^46+12x^48+1x^80

The gray image is a code over GF(2) with n=344, k=9 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.