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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+177x^48+454x^50+72x^51+617x^52+172x^53+848x^54+472x^55+1052x^56+596x^57+960x^58+504x^59+864x^60+180x^61+592x^62+40x^63+284x^64+12x^65+178x^66+70x^68+40x^70+6x^72+1x^84

The gray image is a code over GF(2) with n=228, k=13 and d=96.
This code was found by Heurico 1.16 in 4.71 seconds.