The generator matrix

1 0 0 0 1 1 1 2 1 1 2 1 1 2 1 0 1 0 0 1 2 0 2 1 0 1 0 1 2 1 2 2 0 1 0 2 1 1 1 0 2 1 2 1 1 1 0 1 0 2 1 1 1
0 1 0 0 0 0 0 0 1 1 1 1 1 1 2 1 3 2 1 2 1 2 2 3 1 3 1 2 1 2 1 1 1 1 1 1 0 0 0 0 2 3 1 3 2 2 1 0 1 1 0 1 0
0 0 1 0 1 2 3 1 0 1 1 2 3 0 2 1 3 0 0 0 2 1 1 1 2 2 3 1 3 3 2 0 2 0 2 2 2 1 3 1 1 2 0 0 1 3 0 0 1 1 1 2 0
0 0 0 1 2 1 3 3 1 3 0 0 2 3 3 1 2 1 2 0 3 0 3 3 2 0 3 2 0 3 2 1 3 3 1 1 3 0 2 2 0 3 0 1 0 2 2 1 0 2 1 3 0

generates a code of length 53 over Z4 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+14x^49+39x^50+54x^51+41x^52+26x^53+20x^54+20x^55+15x^56+6x^57+2x^58+2x^59+1x^60+3x^66+4x^67+6x^68+2x^69

The gray image is a code over GF(2) with n=106, k=8 and d=49.
This code was found by Heurico 1.10 in 0 seconds.