The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1  1 X^2+X  1 X+2  1 X+2  1  1  0  1  2  1  1  1  1  0  0  1 X^2+2 X^2  1  X X^2+X+2  1 X^2+X+2  1 X^2+2  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+1  1 X^2 X+1  1  X  1  X  1  1  2  1  2  1 X^2+3 X+3 X^2+X+1  X X^2+2  1  3  1  1 X+1  0  1 X+1  1 X^2+X+3  X  3 X^2+3 X^2+X+3 X^2+X+3
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2  2 X+2 X^2+X+2 X^2 X^2+2 X^2 X^2+X X+2  0 X^2 X+2 X^2+2 X^2 X^2+X+2 X+2  X X^2  0  X X+2 X^2+X+2 X^2+X+2  2 X^2+X X^2+X+2  X X^2+X X^2 X^2+X X+2 X^2+X  X X^2+X  0
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  0  0  0  0  2  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  2  0  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+157x^40+378x^41+684x^42+564x^43+746x^44+528x^45+502x^46+248x^47+152x^48+50x^49+42x^50+20x^51+16x^52+4x^53+3x^54+1x^62

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 0.172 seconds.