The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+324x^40+796x^41+1293x^42+1172x^43+1400x^44+1184x^45+909x^46+428x^47+425x^48+148x^49+53x^50+40x^51+10x^52+8x^53+1x^54

The gray image is a code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.16 in 0.422 seconds.