The generator matrix

 1  0  0  1  1  1  X  1  1  0  1  2  1  X  0  1  X  1  2  1  1  0  1  0  1  1  1  1  0  1  1  0  X  2 X+2  1  0  1  X  1  1  0  1 X+2  1  1  1 X+2 X+2  1  1  2  1  2  1
 0  1  0  0  1 X+3  1  0 X+2  1 X+1  2  3  1  1 X+3 X+2 X+1  1  2  2 X+2 X+3  1 X+2  1  X  2  1  X X+3  1  1  1 X+2 X+1 X+2  2  X X+3  2  1  0  1  X  3  0  1  1  1  3  1 X+2  2  0
 0  0  1  1  1  0  1  1  X  2  0  1 X+3 X+3 X+1 X+3  1 X+2 X+2 X+2 X+3  1  X  0  2  3 X+1  3 X+3  2  3 X+3  3  2  1  X  1  2  1  1 X+3  X X+2  X X+1  X  0 X+1 X+1 X+2 X+2 X+2  1  1  0
 0  0  0  X  0  0  0  2  0 X+2  X  X  X  X  2 X+2 X+2 X+2  0  X  X  2  2  X  0 X+2  X  0 X+2 X+2  2  2  2  2  X X+2  0  2 X+2  X  2  X  X  0  2  X  X  X  X  X  X  0  2  0  0
 0  0  0  0  X X+2  2  X X+2  X  0 X+2  2  X  2  0  X  2  0  2  2  0 X+2  X  0 X+2  X  0  2  X  0  X  X X+2  0 X+2  X  0  0 X+2  2  0 X+2  0 X+2  X  X X+2  2  X X+2 X+2 X+2  2  0
 0  0  0  0  0  2  2  0  2  0  2  0  0  2  0  2  2  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  2  0  0  2  2  0  2  0  0  2  2  0  0  2  0  2  0  0  0  0  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+55x^46+146x^47+384x^48+718x^49+748x^50+1136x^51+996x^52+1622x^53+1357x^54+1886x^55+1476x^56+1868x^57+1097x^58+1110x^59+622x^60+474x^61+296x^62+186x^63+91x^64+50x^65+27x^66+14x^67+10x^68+4x^69+4x^70+2x^71+4x^72

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 9.67 seconds.