The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  2  2  2  X  0  X  X  1  2  1  0  1  1  1  X  0  1  X  1  X
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  0  0  2 X+2 X+2  2  X X+2 X+2  0  0 X+2  X  0  X  2  X  X  X  X  X  X X+2  2  X X+2  0  X  0  2  2  2  X X+2  2  2  2  X X+2
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  X  0  2  2  0  0  2 X+2  X X+2  2 X+2  0 X+2  X X+2  X  0  X  X X+2  2  0  2  X  2  X  0  2  X  0 X+2  0  0  X X+2  0  X  X
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  2  2  X X+2  2  X  X  0 X+2 X+2  0 X+2  0  0  0 X+2 X+2 X+2  0  0  2 X+2  0  X  0 X+2  0  X  2  0  2  2  X  2 X+2 X+2  X  X X+2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  2  0  0  2  0  2  2  0  2  0  0  0  2  2  0  0  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  0  2  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  2  0  0  0  2  0  0  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+183x^46+20x^47+375x^48+60x^49+603x^50+236x^51+861x^52+444x^53+1127x^54+500x^55+1099x^56+468x^57+771x^58+260x^59+546x^60+52x^61+301x^62+8x^63+169x^64+81x^66+17x^68+5x^70+3x^72+1x^74+1x^80

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 53.6 seconds.