The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+246x^49+1534x^50+3400x^51+7086x^52+12542x^53+20956x^54+28198x^55+37800x^56+38282x^57+37367x^58+29190x^59+21691x^60+12240x^61+6806x^62+2868x^63+1201x^64+440x^65+181x^66+70x^67+25x^68+8x^69+4x^70+2x^71+4x^72+2x^77

The gray image is a code over GF(2) with n=456, k=18 and d=196.
This code was found by Heurico 1.16 in 464 seconds.