The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+248x^51+848x^52+2272x^53+2752x^54+3794x^55+3821x^56+5190x^57+4269x^58+4332x^59+2127x^60+1600x^61+800x^62+410x^63+186x^64+54x^65+34x^66+16x^67+9x^68+4x^69+1x^74

The gray image is a code over GF(2) with n=456, k=15 and d=204.
This code was found by Heurico 1.16 in 8.74 seconds.