The generator matrix

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

generates a code of length 48 over Z4 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+120x^34+70x^35+461x^36+466x^37+929x^38+1014x^39+1663x^40+1864x^41+2606x^42+3042x^43+3561x^44+4378x^45+4481x^46+5414x^47+4835x^48+5470x^49+4716x^50+4654x^51+3763x^52+3202x^53+2704x^54+1814x^55+1585x^56+880x^57+758x^58+346x^59+327x^60+114x^61+181x^62+30x^63+60x^64+10x^65+16x^66+1x^70

The gray image is a code over GF(2) with n=96, k=16 and d=34.
This code was found by Heurico 1.10 in 140 seconds.