The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X X^2 X^2 X^2  X  X  X X^2  X X^2  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  2  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  0  2  2  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  0  2  2  0  0  0  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  0  2  0  2  2

generates a code of length 57 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+24x^53+42x^54+176x^56+80x^57+128x^58+24x^61+20x^62+15x^64+2x^70

The gray image is a code over GF(2) with n=456, k=9 and d=212.
This code was found by Heurico 1.16 in 0.797 seconds.