The generator matrix

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

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+127x^40+708x^41+1716x^42+2696x^43+3727x^44+4792x^45+5388x^46+4894x^47+3750x^48+2616x^49+1268x^50+558x^51+367x^52+104x^53+28x^54+10x^55+10x^56+4x^57+2x^59+2x^60

The gray image is a code over GF(2) with n=368, k=15 and d=160.
This code was found by Heurico 1.16 in 6.89 seconds.