The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+73x^38+684x^39+1402x^40+2860x^41+3764x^42+5092x^43+5158x^44+5394x^45+3396x^46+2732x^47+1337x^48+530x^49+184x^50+100x^51+38x^52+14x^53+7x^54+2x^57

The gray image is a code over GF(2) with n=352, k=15 and d=152.
This code was found by Heurico 1.16 in 5.92 seconds.