The generator matrix

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

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+442x^36+1712x^37+5064x^38+9744x^39+19839x^40+29064x^41+42523x^42+44356x^43+43175x^44+30312x^45+19947x^46+9168x^47+4546x^48+1384x^49+585x^50+180x^51+59x^52+24x^53+9x^54+8x^55+2x^56

The gray image is a code over GF(2) with n=344, k=18 and d=144.
This code was found by Heurico 1.16 in 340 seconds.