The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1 15  1  1  1  1 20  1  1  1 15  1  1  1 10  1  1  1  1 10  1  1  1  1  1  1  1  1  1  1  1  1  5  1  1  1  1  1  1  1 20  1  0  1  1  1  0  1 10  1 15 20  1  0  1  1  1  1  5  1  5  1 10  1
 0  1  0  0  5 15  5 16  1 18 16  1 11 23  7 14  1 14  7  1 22  8 18 24  1 12 12 24  1  4  3 13  1 11 15 24  1  1  8 16  2 13 21  9 10  6 22  6 20 14  1 24  2 23 18  1 12  8  1 18 10  4  2  4  1 13  1 20  1  1  8  0 21 11 10 15  1 22  1 18  0  0
 0  0  1  1 22 14  8 13 24  5  2 11 15 22  7  7  3 13 23 16 16 19 23  1  9 14 20 24  2  0  6  8 24 16 23 21 19 23  4 12  9 10  0 10 20 13  0  9  9 14  2  2  6 17  5 20  4 10 16 22  1 17  6 13 18 15 20 14  3 21  6  1 12 14  9  8 10  0 17  7  1 18
 0  0  0 15 15 10 10 10 10  0 15 15  0  0 10 20  5 15 15 10  0 20  5  0 10  0 20  5  0 20 10 15 20 20 20 15  0 15  0 20 10 10 10  0 20 20 15 15  5 10 15  0  5 10 15  5 15  5 15 20 10 15 20 10 20 20 20 20  5  0  0  5  5  5  0 15 15  5  5 15 10  5

generates a code of length 82 over Z25 who´s minimum homogenous weight is 311.

Homogenous weight enumerator: w(x)=1x^0+460x^311+900x^312+1180x^313+600x^314+1124x^315+2060x^316+2660x^317+2660x^318+1260x^319+1548x^320+3740x^321+3480x^322+3820x^323+1540x^324+2228x^325+4340x^326+4420x^327+4280x^328+1300x^329+2420x^330+3860x^331+3800x^332+4240x^333+1560x^334+2420x^335+3520x^336+2880x^337+3020x^338+920x^339+720x^340+1740x^341+1500x^342+800x^343+320x^344+108x^345+280x^346+360x^347+24x^350+4x^355+8x^360+4x^365+12x^370+4x^380

The gray image is a code over GF(5) with n=410, k=7 and d=311.
This code was found by Heurico 1.16 in 12.4 seconds.