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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+27x^40+68x^42+320x^43+75x^44+12x^46+8x^48+1x^84

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 0.063 seconds.