The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+164x^46+48x^47+521x^48+272x^49+1000x^50+700x^51+1586x^52+1276x^53+1852x^54+1552x^55+1971x^56+1288x^57+1566x^58+668x^59+922x^60+300x^61+368x^62+40x^63+183x^64+70x^66+25x^68+4x^70+4x^72+3x^76

The gray image is a code over GF(2) with n=220, k=14 and d=92.
This code was found by Heurico 1.16 in 14.3 seconds.