The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  X  1  1  1  1 3X  1  1  1  1  1  1  1  1 4X  1  1  1  0  1  1  1  1  1  1  1  1  X  X  1 4X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 4X  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1
 0  1  1  2 3X+4  3  0 3X+1  2 3X+4  3  1  0 3X+4  3  1 3X+1  2 4X+1 X+2 X+3  1 4X+1 X+2  X 4X+4  1 2X 3X+1 3X+3 4X+4  X  1  3 3X+1  1 2X+2  0 2X+4  1 2X+2 4X+4 2X+3 X+4  1 2X+3  1 4X  1  1 3X+2  1 2X+3 3X+4 4X+3 X+2  2 2X 2X 3X+1 4X+2 4X+1 2X+2 4X+3 2X+1 X+2  1 X+1 3X+2  3 3X+2 2X+1 4X+4 X+2 3X+1 2X  4 2X+1  1  X  2  0
 0  0 3X  0 3X 2X  0 4X 2X 4X  X 3X 2X  0 3X 3X 3X  0  X  0  X  0 4X 2X 4X 2X 2X  X  0 3X 2X 2X  0 4X 4X 4X 3X 4X 2X 2X 4X  X 4X  X  X 2X 2X 3X  X 3X 4X 4X  0 4X  0 3X 2X 3X  X  X  X 4X  X 2X  0 2X 2X 2X 3X  X 3X  0 3X  0 3X 4X  X 2X  0 3X 3X  X
 0  0  0  X 3X  X 2X 3X  0 2X 3X  X 2X 3X  X 3X 4X 2X  X 4X 2X 4X 4X 4X 2X  X 3X 4X 4X 2X 2X 4X 3X 3X  X 3X 4X  0 3X  0 4X  0  X  X  0 3X 4X 2X 4X  0  0  0  X  0 2X  0 3X  X  0 3X 4X 3X  X 2X  X 2X 2X  0  X 4X 2X  0  X 3X 2X 3X 2X 3X 2X 4X  0 3X

generates a code of length 82 over Z5[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+616x^315+300x^316+640x^319+2616x^320+440x^321+420x^324+2136x^325+520x^326+400x^329+2008x^330+600x^331+880x^334+1980x^335+480x^336+160x^339+924x^340+160x^341+296x^345+8x^350+12x^355+4x^360+4x^365+12x^370+4x^375+4x^380

The gray image is a linear code over GF(5) with n=410, k=6 and d=315.
This code was found by Heurico 1.16 in 0.663 seconds.