The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2X+2) 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.