The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+2x^44+46x^45+2x^46+8x^47+2x^49+1x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=360, k=6 and d=176.
This code was found by Heurico 1.16 in 0.047 seconds.