The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+55x^24+124x^25+239x^26+324x^27+427x^28+566x^29+752x^30+970x^31+1158x^32+1318x^33+1450x^34+1478x^35+1421x^36+1446x^37+1218x^38+1026x^39+755x^40+546x^41+501x^42+270x^43+143x^44+92x^45+62x^46+28x^47+7x^48+4x^49+2x^50+1x^52

The gray image is a code over GF(2) with n=70, k=14 and d=24.
This code was found by Heurico 1.10 in 5.5 seconds.