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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+82x^46+138x^47+202x^48+288x^49+350x^50+496x^51+630x^52+892x^53+1062x^54+1404x^55+1780x^56+1766x^57+1748x^58+1460x^59+1116x^60+860x^61+598x^62+478x^63+341x^64+232x^65+164x^66+108x^67+86x^68+56x^69+25x^70+12x^71+4x^72+2x^73+2x^74+1x^86

The gray image is a code over GF(2) with n=228, k=14 and d=92.
This code was found by Heurico 1.16 in 16.8 seconds.