The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  X  X  1  X 2X+2 2X+2 2X+2  1  1  X  X  X  X  1  1  X  X  X  X  X 2X+2  1
 0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0
 0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0  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+3x^44+50x^45+3x^46+4x^49+1x^50+2x^57

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 0.031 seconds.