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

generates a code of length 53 over Z49 who´s minimum homogenous weight is 294.

Homogenous weight enumerator: w(x)=1x^0+162x^294+402x^301+480x^308+390x^315+14406x^318+228x^322+246x^329+144x^336+150x^343+120x^350+60x^357+12x^364+6x^371

The gray image is a code over GF(7) with n=371, k=5 and d=294.
This code was found by Heurico 1.16 in 0.253 seconds.