The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+100x^36+718x^37+2114x^38+5192x^39+10519x^40+19582x^41+29608x^42+40792x^43+44321x^44+41360x^45+29884x^46+19956x^47+10258x^48+4768x^49+1898x^50+676x^51+299x^52+66x^53+14x^54+4x^55+6x^56+2x^57+2x^58+4x^59

The gray image is a code over GF(2) with n=352, k=18 and d=144.
This code was found by Heurico 1.16 in 334 seconds.