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.