The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  7  7  1  1  1  1  1  1  1  1  1  1  7  1  1  1
 0  7  0  0  0  0  0  0  7  7 35 14  7 28 14 21 14 28 28 42 35 28 14 21 35 28  0 35 14 35 35 14 14 28  0 14 14 21 35 35 35 21 28 35 14  0 14 42  0 42 42 14  0 14 35 21 42  7 35 42 21 14 35  7  7 42 42  0 28  0 35  0  7 42 42  0  7  7  0
 0  0  7  0  0  7  7 28 35 28 14 42 14  7 35  7 28  0 21 28  0 14 42  7  0 35 42 14 21 21  7 35 28 28  0 21 14  0  7 42 14 42 14 42 42  0 35 21 21 14 42 42 35 21 28 21  0 28 35  7 21 42 28 28 14 21 35 42  0 42  7  7 35  7 28  7  0 28  0
 0  0  0  7  0 35 28 21 35  0 42 14 35  7  0 35  0 21 28  7 14 21 21 21 35 35 28 42  7 21 35 35  0  0 28 42 42 21  0 14 28 35 14 28 28  7 14  0 35  0 35  7 35  7 14 14 14  7  0  7  7 21 28 21  7 35 21 28 14 21 14 21  7  7 28 14 42 35  0
 0  0  0  0  7 35  7 14 35 28 14 42 42  0 14  0 42 35  7 42 21  7 28 14 14 28  7  7  7 21 28 14 14 42 35 21 35  0  0 28 42 14  0 35  0 35 35 14 35 35 35 28 28 14 14 14 35 14  7  7 42  0  0  0  7 21 42  0 21 42 21  7 28 28 14 35 21  0 42

generates a code of length 79 over Z49 who´s minimum homogenous weight is 434.

Homogenous weight enumerator: w(x)=1x^0+288x^434+1086x^441+1524x^448+1704x^455+294x^456+1914x^462+5292x^463+1770x^469+31752x^470+1764x^476+63504x^477+1668x^483+1656x^490+1320x^497+1008x^504+618x^511+288x^518+156x^525+36x^532+6x^546

The gray image is a code over GF(7) with n=553, k=6 and d=434.
This code was found by Heurico 1.16 in 18.6 seconds.