The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+90x^45+178x^46+470x^47+356x^48+710x^49+487x^50+774x^51+334x^52+406x^53+163x^54+98x^55+10x^56+10x^57+2x^59+2x^60+2x^62+1x^64+1x^66+1x^70

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 98.6 seconds.