The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+272x^40+1580x^41+3020x^42+5252x^43+7323x^44+9976x^45+10828x^46+10004x^47+7437x^48+5158x^49+2662x^50+1414x^51+402x^52+148x^53+48x^54+2x^56+2x^57+2x^58+2x^59+3x^60

The gray image is a code over GF(2) with n=368, k=16 and d=160.
This code was found by Heurico 1.16 in 24.6 seconds.