The generator matrix

 1  0  0  1  1  1  X X+2  1  1  1  2  1  0  2  1  1  2  1  1  2  2  1  1  1  X  X  2  0  1  1  1 X+2  1  0  1  1  0  X X+2  1  X  0  1  2  1  0  1  1 X+2  1 X+2 X+2  2 X+2  1  1
 0  1  0  0  1 X+3  1  0  2  0 X+3  1 X+1  1  2 X+2 X+3  1  3 X+2  1  1  0  3 X+3  2  1  2  1 X+3 X+1 X+2  1  0  1 X+2  X  1  1 X+2  3  1  1  0  0 X+1 X+2  X  3  1  1  2  1  1  1  3  0
 0  0  1  1  1  0  1  1  X X+3 X+1  1  X  0  1  3  2 X+3 X+1  0  2  3  3  2  3  1  3  1 X+2  1  2 X+3  3  1  X  X  2  X  2  1 X+3 X+1 X+3 X+3  1  X  1 X+1  2 X+3  X  1 X+2 X+1  0  1  0
 0  0  0  X  0  0  0  2  2 X+2  2  2  0 X+2 X+2  0  X X+2  X  X  X X+2  2  X  0  X  0  2  2 X+2  0  2 X+2  2  X  X X+2  X  0  2 X+2  2  2  2  0 X+2 X+2  0  2  2 X+2  0  X  X  2  0  0
 0  0  0  0  X X+2  2  2  2  2 X+2  2  X  X  X X+2  2 X+2  X X+2  0  2 X+2  X  2  0  X  X  X X+2  0  2  0  0 X+2  0  0  0 X+2  X  2  2  0  0 X+2 X+2  X  X X+2  X  0 X+2  2  2 X+2  X  0
 0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  2  0  2  0  0  2  2  0  0  0  0  0  0  2  2  2  0  0  0  2  2  0  2  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+61x^48+204x^49+409x^50+570x^51+880x^52+1052x^53+1152x^54+1490x^55+1578x^56+1618x^57+1579x^58+1512x^59+1398x^60+966x^61+658x^62+532x^63+318x^64+178x^65+97x^66+54x^67+42x^68+14x^69+6x^70+2x^71+10x^72+3x^74

The gray image is a code over GF(2) with n=228, k=14 and d=96.
This code was found by Heurico 1.16 in 10.6 seconds.