The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+98x^49+402x^50+594x^51+1046x^52+954x^53+1466x^54+1370x^55+1744x^56+1298x^57+1761x^58+1228x^59+1456x^60+958x^61+800x^62+462x^63+407x^64+140x^65+108x^66+48x^67+18x^68+8x^69+6x^70+8x^71+1x^74+2x^75

The gray image is a code over GF(2) with n=228, k=14 and d=98.
This code was found by Heurico 1.13 in 3.72 seconds.