The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X+2  1  1 X^2+2  1  1  1  1  0 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1 X^2+2 X+2  0  2 X^2+X X^2+X+2  1  1  1  1 X^2+2  X X^2  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X+1  3  1  1 X+2 X^2+2 X^2+X X+2  0  2 X^2+X+3 X^2+1 X+1 X^2+1 X+3 X^2+3  1  1  1  1  1  1 X^2+X+2  X X^2+2 X^2  X X^2+X+2  X  X  0
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  2  2
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  0  2  2  0  2  2  0  2  2  2  0  0  0  2  0  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+108x^53+238x^54+288x^55+290x^56+280x^57+250x^58+224x^59+220x^60+108x^61+22x^62+1x^64+16x^65+2x^74

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 0.141 seconds.