The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) 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 0.062 seconds.