The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+28x^45+207x^46+15x^48+4x^53+1x^62

The gray image is a code over GF(2) with n=368, k=8 and d=180.
This code was found by Heurico 1.16 in 91.8 seconds.