The generator matrix

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

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+108x^45+279x^46+306x^47+539x^48+608x^49+627x^50+510x^51+465x^52+240x^53+177x^54+122x^55+66x^56+12x^57+12x^58+6x^59+9x^60+8x^61+1x^74

The gray image is a code over GF(2) with n=400, k=12 and d=180.
This code was found by Heurico 1.16 in 0.297 seconds.