The generator matrix

 1  0  1  1  1 3X+2  1  1 2X+2  1  1 2X  1  1  X  1  1  1  1  X  1  1  2 X+2 2X+2 3X 2X X+2  X 2X 3X+2 2X 3X+2  0  1  1  1  1  1  1  0 2X+2 3X
 0  1 X+1 3X+2  3  1 2X X+3  1 2X+2 X+1  1  X 2X+1  1  2 2X+3 X+2 3X+3  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1 2X 3X+3  1 2X+2  3 3X+3  0  1  1
 0  0  2  2 2X  2 2X+2 2X+2 2X 2X  0 2X+2  2 2X  2 2X+2  2  0  0  2 2X 2X+2 2X+2  0  0 2X  2 2X  0 2X 2X+2 2X+2 2X  2  2 2X 2X+2 2X  0  0  2  0 2X
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X  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+308x^40+304x^41+244x^42+336x^43+355x^44+208x^45+204x^46+48x^47+34x^48+4x^52+1x^60+1x^64

The gray image is a code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 18.5 seconds.