The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1 2X+2  2  2  1  1 X+2  1 3X+2  1  1 2X  1  1  1  0 3X+2  X  1 3X+2  1  1 3X  1  X  2  1 2X+2  1  1  1 X+2 3X+2  1  1  1  1 2X+2  2  1  1  0  1  1 3X 3X+2  1
 0  1  0 2X 2X+3  3  1  X 3X+3 3X X+3  1  X  1 3X+1  0  1 2X+2  X 2X+1 X+2  1 2X+3 3X+1  X  1  2  1  2  1 2X+2 3X+3  1 X+3  1  0 3X+2  1  1 3X+2  1 X+2  1 2X 2X  X X+1  2 X+2  1  2 3X X+2  3  2  0  0
 0  0  1 3X+1 X+1 2X 3X+1 3X  1 2X+1  X  X  1 3X+3 2X+2 3X+2 X+2  3  1  1 3X+1 2X+3 X+2 X+1  2 2X+2  1 2X+1 2X+2 3X+3 X+1 X+1  2  0  X  1 2X+3 2X+3 3X  0 X+3  1 X+1 2X+1 2X+3 3X+3  X  1  1 2X 2X  1 3X+2  X  1  1  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+100x^53+508x^54+692x^55+767x^56+544x^57+482x^58+372x^59+230x^60+124x^61+99x^62+80x^63+65x^64+8x^65+22x^66+1x^70+1x^72

The gray image is a code over GF(2) with n=456, k=12 and d=212.
This code was found by Heurico 1.16 in 0.203 seconds.