The generator matrix

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

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+30x^45+207x^46+15x^48+2x^61+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 0.063 seconds.