The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  X  1  1  X  2  1  2  1 X+2  1  2  0  1  2  X  1  1  2  1  1  1  0  2  1  1  1  1  X  1 X+2  2  1  X  1  1  1 X+2  1  1  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1  1 X+2  1  0  0  1 X+1  1 X+3  1  1  2  X  1 X+1  X X+2  2 X+2  0  1  1 X+3 X+3  1 X+1  1  X  2  1 X+1  1 X+2  1  3  1  1  3  1
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  2  X  0  1  1 X+1  X X+3  0  1 X+1 X+2 X+2  1  3 X+2  X  1  1  3  0  0  3 X+2 X+3  1  0  2  X  1  1  3  2  0 X+3  2 X+1  1 X+1  1
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  0  0  0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  0  0  0  0  2  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  0  0  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  2  2  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  0  2  2  2  0  2  2  2  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  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+65x^46+190x^47+219x^48+638x^49+634x^50+1460x^51+976x^52+1732x^53+1194x^54+2196x^55+1256x^56+1856x^57+930x^58+1328x^59+539x^60+604x^61+219x^62+190x^63+64x^64+34x^65+20x^66+12x^67+12x^68+10x^70+4x^72+1x^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 9.59 seconds.