The generator matrix

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

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+100x^46+422x^47+1008x^48+1924x^49+2700x^50+4396x^51+5715x^52+7878x^53+9565x^54+11880x^55+12333x^56+14214x^57+13016x^58+12258x^59+9819x^60+8366x^61+5690x^62+4084x^63+2416x^64+1558x^65+830x^66+482x^67+218x^68+108x^69+65x^70+14x^71+10x^72+2x^74

The gray image is a code over GF(2) with n=228, k=17 and d=92.
This code was found by Heurico 1.13 in 187 seconds.