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

generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+153x^52+64x^54+192x^55+385x^56+640x^57+128x^58+192x^59+218x^60+61x^64+13x^68+1x^104

The gray image is a code over GF(2) with n=456, k=11 and d=208.
This code was found by Heurico 1.16 in 1.66 seconds.