The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+26x^23+122x^24+256x^25+440x^26+592x^27+794x^28+1230x^29+1523x^30+1822x^31+2331x^32+2718x^33+2899x^34+3028x^35+2998x^36+2748x^37+2452x^38+1986x^39+1576x^40+1156x^41+740x^42+540x^43+344x^44+198x^45+129x^46+70x^47+26x^48+14x^49+9x^50

The gray image is a code over GF(2) with n=70, k=15 and d=23.
This code was found by Heurico 1.10 in 20.9 seconds.