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  2  2  X  X  2  X  1  1  0  0  1  0  0  2  X  X  1  1  X  X  2  1  X  1
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  0  0  2 X+2 X+2  2  2  X X+2  0 X+2  2 X+2  0  2  0 X+2  X  X  X  X  X X+2  0  2  0  2 X+2  0  0  0  0  X  2 X+2 X+2  2  X  0  0  0
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  X  0  2  2  0  0 X+2  2 X+2 X+2  X  2  2 X+2 X+2  2 X+2  X  X  0  0  2  0  2  2  X  0  2  X  X  2 X+2  2 X+2  2  0 X+2  2 X+2  0 X+2
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  2  2  X X+2  2  X  2  X  0 X+2 X+2  2  0  0 X+2  2 X+2  0  0 X+2 X+2 X+2  0  2 X+2  2  X  X  X  0  X  0  0  0  0 X+2  X  0 X+2 X+2  0
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  2  0  2  0  0  0  2  2  2  0  0  0  0  2  2  2  0  0  2  0  0  0  2  0  2  2  2  2  2  0  2  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  2  0  2  0  0  2  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0  2  2  2  0  0  0  2  2  0  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2  0  2  2  2  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  0  2  0  0  0  0  2  2  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+229x^48+4x^49+408x^50+76x^51+601x^52+236x^53+816x^54+444x^55+1045x^56+548x^57+1028x^58+420x^59+887x^60+228x^61+514x^62+84x^63+345x^64+8x^65+154x^66+77x^68+22x^70+11x^72+2x^74+3x^76+1x^80

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 4.8 seconds.