The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1 X^2+2  1  1 X+2  1  X  1  1  1  1  X  X
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X+3 X^2+X  1 X^2+2  1 X^2+1 X+2  1 X^2+1 X^2+X X^2+3 X^2+X+3  0  2  X X^2+X+2
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  2  0  2  0  0  2
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  2  2  0  2
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  2  0  0  2  2  0

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+80x^39+226x^40+176x^41+480x^42+152x^43+477x^44+144x^45+208x^46+80x^47+12x^48+8x^51+3x^52+1x^56

The gray image is a code over GF(2) with n=344, k=11 and d=156.
This code was found by Heurico 1.16 in 0.062 seconds.