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  X  1 X^2  1  1  1  1  1  1  1  X  1  1  X  1  1  0  1  1  X  1  X  1  1  1  X
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2 X+2 X+2  0 X^2 X+2 X^2+X X^2 X^2+X+2  2 X^2+2 X^2 X^2+X  X X+2 X^2+X  X  0 X+2 X^2+X+2 X^2+X+2  0 X^2+X X^2+2 X+2 X^2 X+2 X^2+X X^2+2 X^2  X X^2+X  0  2  2  X X^2+2 X^2+2  2  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X X^2+2  0 X^2+X X+2  2  0 X^2+X+2 X^2+X X^2+2 X^2+2 X^2+X X+2 X^2+2 X^2+2 X^2+X+2 X+2  0 X+2  0  2 X^2+X+2 X+2 X+2 X^2  0  2  X X^2+X+2 X^2+X X^2  2  2  0 X^2+X X^2+X X+2  2 X^2 X^2  X  0 X+2 X^2+X  2 X^2+X X^2+X
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  2  2  0  0  2  0  2  0  0  2  2  0  0  2  0  2  2  2  2  0  2  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+148x^53+136x^54+302x^55+246x^56+442x^57+278x^58+244x^59+80x^60+92x^61+16x^62+42x^63+9x^64+6x^65+1x^66+4x^67+1x^98

The gray image is a code over GF(2) with n=456, k=11 and d=212.
This code was found by Heurico 1.16 in 0.344 seconds.