The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+119x^36+900x^37+2808x^38+5528x^39+9864x^40+15206x^41+19686x^42+22062x^43+20915x^44+15204x^45+9771x^46+5502x^47+2277x^48+778x^49+302x^50+90x^51+40x^52+6x^53+7x^54+2x^55+2x^58+2x^61

The gray image is a code over GF(2) with n=344, k=17 and d=144.
This code was found by Heurico 1.16 in 82.2 seconds.