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

generates a code of length 78 over Z49 who´s minimum homogenous weight is 427.

Homogenous weight enumerator: w(x)=1x^0+240x^427+1038x^434+1440x^441+1626x^448+294x^450+1842x^455+5292x^457+1860x^462+31752x^464+1830x^469+63504x^471+1584x^476+1524x^483+1452x^490+1158x^497+672x^504+342x^511+144x^518+48x^525+6x^532

The gray image is a code over GF(7) with n=546, k=6 and d=427.
This code was found by Heurico 1.16 in 18.3 seconds.