The generator matrix

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

generates a code of length 50 over Z4 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+26x^35+76x^36+222x^37+414x^38+624x^39+895x^40+1172x^41+1558x^42+1948x^43+2450x^44+3156x^45+3576x^46+4096x^47+4642x^48+5088x^49+5130x^50+4858x^51+4917x^52+4428x^53+3933x^54+3276x^55+2535x^56+2016x^57+1430x^58+1124x^59+741x^60+496x^61+302x^62+164x^63+111x^64+60x^65+34x^66+12x^67+15x^68+2x^69+7x^70+1x^76

The gray image is a code over GF(2) with n=100, k=16 and d=35.
This code was found by Heurico 1.10 in 149 seconds.