The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  0  1 X+2 X+2  1  1  X  1  1  1  1  0  1  2  0  0  X  1  1  1  X  2  X  1  2  0  X  1  1  1 X+2  1  1  1  X  X  1  1  1  0  X  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  3  1  1  1  2  2 X+3  2  3  3  X X+2  1  1  1 X+2  1 X+1 X+3  1  0  X  0  X X+2  1 X+1  1  X  1  2  1 X+1  1  0 X+1  3  X  2  1  2  X  3 X+1  2
 0  0  1  0  0  0  1  1  1  3  1  2  X  1 X+1  2  3  2  1 X+2  0 X+2  1  1 X+2 X+3  X  1 X+2 X+3  2 X+3 X+2  0  X  0  1  X  3 X+3  3 X+1 X+2  3 X+2  3  1 X+1  3  X X+2 X+1  X X+1  1  2 X+1
 0  0  0  1  0  1  1  0  3  2 X+1 X+3 X+2  3  X X+3 X+2  1 X+1 X+3  2  3 X+2  3 X+3  1  0  1  0 X+2  1  0 X+2  1  2  1  3  X  1  X X+3  3 X+1 X+1 X+1  1  1  3 X+2 X+3  1  2  X  3 X+1 X+1  2
 0  0  0  0  1  1  2  3  1  0 X+1 X+3 X+1  0  1  2  X X+1 X+2  0 X+2  3 X+1 X+3  2 X+3  3 X+2  X X+3 X+2  2  1  0 X+3 X+3  3 X+3  0 X+2  0 X+3 X+3  1  3 X+2  2 X+1  2 X+2 X+3 X+2  1  2 X+1  2  2
 0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  0  0  0  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  0  2  0  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+520x^48+688x^49+1892x^50+1564x^51+3975x^52+3180x^53+5876x^54+4236x^55+8045x^56+5068x^57+8314x^58+4500x^59+6358x^60+3188x^61+3752x^62+1604x^63+1569x^64+404x^65+480x^66+128x^67+131x^68+16x^69+36x^70+9x^72+2x^74

The gray image is a code over GF(2) with n=228, k=16 and d=96.
This code was found by Heurico 1.13 in 185 seconds.