The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^40+128x^42+512x^43+226x^44+26x^48+14x^52+1x^80

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 0.532 seconds.