The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+144x^48+220x^50+324x^52+254x^54+300x^56+208x^58+212x^60+164x^62+139x^64+36x^66+24x^68+14x^70+8x^72

The gray image is a code over GF(2) with n=112, k=11 and d=48.
This code was found by Heurico 1.16 in 0.597 seconds.