The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+16x^42+34x^43+95x^44+348x^45+66x^46+368x^47+29x^48+4x^49+45x^50+14x^51+3x^52+1x^90

The gray image is a code over GF(2) with n=368, k=10 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.