The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+226x^51+982x^52+1946x^53+3073x^54+3638x^55+4368x^56+4804x^57+4292x^58+3688x^59+2670x^60+1470x^61+869x^62+374x^63+215x^64+96x^65+30x^66+10x^67+12x^68+4x^69

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 9.11 seconds.