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

generates a code of length 81 over Z49 who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+624x^448+1260x^455+1476x^462+294x^468+1872x^469+5292x^475+1764x^476+31752x^482+1782x^483+63504x^489+1770x^490+1572x^497+1692x^504+1188x^511+840x^518+534x^525+270x^532+126x^539+36x^546

The gray image is a code over GF(7) with n=567, k=6 and d=448.
This code was found by Heurico 1.16 in 20.7 seconds.