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

generates a code of length 82 over Z49 who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+108x^448+696x^455+1308x^462+1632x^469+294x^474+1806x^476+5292x^481+1746x^483+31752x^488+1824x^490+63504x^495+1656x^497+1518x^504+1602x^511+1104x^518+840x^525+558x^532+270x^539+108x^546+30x^553

The gray image is a code over GF(7) with n=574, k=6 and d=448.
This code was found by Heurico 1.16 in 19.4 seconds.