The generator matrix

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

generates a code of length 50 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+266x^45+907x^46+1556x^47+2090x^48+2380x^49+2362x^50+2286x^51+2019x^52+1318x^53+572x^54+308x^55+211x^56+66x^57+22x^58+6x^59+6x^60+1x^62+4x^63+2x^65+1x^68

The gray image is a code over GF(2) with n=400, k=14 and d=180.
This code was found by Heurico 1.16 in 2.05 seconds.