The generator matrix

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

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+35x^46+64x^47+163x^48+262x^49+466x^50+520x^51+627x^52+806x^53+754x^54+884x^55+836x^56+746x^57+618x^58+496x^59+355x^60+198x^61+148x^62+68x^63+51x^64+32x^65+23x^66+16x^67+14x^68+4x^69+3x^70+1x^72+1x^74

The gray image is a code over GF(2) with n=220, k=13 and d=92.
This code was found by Heurico 1.16 in 3.44 seconds.