The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1  1  1
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  2  0 2X 2X+2 2X 2X 2X+2 2X  2 2X 2X+2 2X  2 2X 2X 2X+2  2 2X 2X 2X+2  2  2  2 2X+2  2  0 2X 2X  0 2X
 0  0 2X+2  2  0 2X+2  2  0 2X  2 2X+2 2X 2X 2X+2  2  2 2X  2 2X 2X+2  2 2X 2X  2  2  0  0 2X+2 2X+2  0  0 2X+2  2 2X  2 2X+2  0  0  0 2X  2 2X+2  2
 0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X  0 2X  0  0 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+13x^40+74x^41+16x^42+304x^43+18x^44+68x^45+14x^46+2x^49+1x^50+1x^74

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 0.062 seconds.