The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+22x^46+44x^47+122x^48+122x^49+175x^50+192x^51+223x^52+238x^53+250x^54+272x^55+269x^56+290x^57+247x^58+308x^59+211x^60+288x^61+226x^62+144x^63+147x^64+66x^65+74x^66+60x^67+37x^68+18x^69+22x^70+4x^71+13x^72+2x^73+7x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=114, k=12 and d=46.
This code was found by Heurico 1.16 in 2.19 seconds.