The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+46x^51+80x^52+68x^53+31x^54+48x^55+64x^56+34x^57+25x^58+18x^59+24x^60+10x^61+3x^62+6x^63+19x^64+10x^65+3x^66+8x^67+2x^69+2x^70+2x^71+4x^72+4x^73

The gray image is a code over GF(2) with n=112, k=9 and d=51.
This code was found by Heurico 1.10 in 0.484 seconds.