The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  2  1  1 2X  X  1  1  1  1  1  X  1  1  1  1  1 2X+2  1  1  1  X  X 2X+2  1  1  1  1
 0  X  0 X+2 2X+2 3X+2  2  X 2X  0 3X+2 3X+2 2X+2 2X+2 3X  X 3X+2  X 3X  X  0 X+2  X X+2 3X 2X X+2 X+2 X+2 3X+2  0  2  0 3X 2X+2  X  X 2X+2 X+2 3X X+2  X 3X+2 X+2 X+2  0
 0  0  2  0 2X+2  0  0 2X  0 2X+2 2X+2 2X+2 2X+2 2X  2 2X+2  2 2X 2X+2 2X  0  0 2X  2  0 2X+2 2X+2 2X+2  2 2X  0 2X+2  0  2  0 2X+2 2X 2X  0  0  2 2X 2X+2  0 2X  0
 0  0  0  2  0  0 2X 2X+2 2X+2 2X+2 2X+2 2X  2 2X+2  0 2X+2  2  0  2 2X 2X 2X+2  2  0 2X  0 2X+2  2 2X  0 2X+2 2X  0  2 2X+2 2X  0 2X+2  2 2X 2X  2  0  0  0  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0  0 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+45x^40+92x^41+203x^42+284x^43+597x^44+418x^45+880x^46+394x^47+598x^48+256x^49+187x^50+66x^51+34x^52+10x^53+7x^54+6x^55+2x^56+8x^57+2x^59+3x^60+2x^62+1x^70

The gray image is a code over GF(2) with n=368, k=12 and d=160.
This code was found by Heurico 1.16 in 0.328 seconds.