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

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+126x^53+166x^54+352x^55+243x^56+414x^57+208x^58+236x^59+118x^60+102x^61+13x^62+36x^63+14x^64+14x^65+4x^66+1x^94

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 0.203 seconds.