The generator matrix

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

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+335x^40+96x^41+808x^42+480x^43+870x^44+288x^45+704x^46+160x^47+311x^48+24x^50+8x^52+9x^56+2x^60

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 3.66 seconds.