The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  0  1  1  0  1  1  1  1  1  5  1  1  1  1  1  1  5  1  1  1  1  1  1  1  1  1  5  1  1  0  1  1  1  1 15  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1 15  1  1  1  1  5  1  1  1  1  1  1
 0  1  1  7 24 18 16  0  7  1 18 14  0 16 14 18  1  7  0  1 16 14 18  7 14  1 12 16 23 12 13  5  1 19  2 10  4 21 18 21 15 13  1 15  1  1  9  1  7 20  1 13  4  1 17 18 23  4 16 15 23 24 16 17  1  9  7 21  3 19  2  4  1 24 16  0  1  1 20 22 23  8 18  0
 0  0 15  0  0  0  0  5 10 15 10 15 10 20  0 10  5 15 10 20 20 15  5  5 20 10  0 20 20 10 10  0  5  0 20 15 15 15 10 10 10  5  0 20 20 10 20 10 15 15 15 15 20 20 15 20 15  5 20 20  0 20  0  5  0 10  0 10  0 20 15 15  5 15  5  0  5 10 20  0  0  5 10  0
 0  0  0  5  0  5 15 15  0 10 10 20 10 10 15  5  0 10 15  0  5  0  5 10 10  5 15  0 10 20 20  0 10 20  5 15  5 15  0  0 10  5  5  5 15 10 20  0 20 20 10  0 10 15  5 15  5 15  5 15  5 10 20  5 15  0  0 10 20 20  5 10  0  0 15 20 15  0 15  0 20 10  0  0
 0  0  0  0 15 15 10 20 20  5 20 20 10  0  0 10 15 15  0  0  0  5 10 20 10 15 20 20 20 15 20  5 15  5 10 20  5 10 10  0 15 15  5  5  0 15 20 15 15  0 10 15 15  5 15 20  0 15 15  5 10 20 10  5  0  5 20  5 20  5 20 10  5 20 15 15  5 15  0 10 15  5 20 10

generates a code of length 84 over Z25 who´s minimum homogenous weight is 310.

Homogenous weight enumerator: w(x)=1x^0+64x^310+20x^314+316x^315+200x^316+320x^317+200x^318+640x^319+420x^320+1620x^321+900x^322+920x^323+2240x^324+392x^325+2700x^326+1440x^327+1480x^328+3680x^329+424x^330+4380x^331+2220x^332+2780x^333+5480x^334+256x^335+5780x^336+3120x^337+3580x^338+7060x^339+240x^340+5880x^341+2700x^342+2780x^343+4540x^344+244x^345+3760x^346+1520x^347+760x^348+1340x^349+160x^350+680x^351+280x^352+180x^355+148x^360+92x^365+72x^370+72x^375+16x^380+12x^385+12x^390+4x^395

The gray image is a code over GF(5) with n=420, k=7 and d=310.
This code was found by Heurico 1.16 in 15.3 seconds.