The generator matrix

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

generates a code of length 84 over Z5[X]/(X^2) who´s minimum homogenous weight is 325.

Homogenous weight enumerator: w(x)=1x^0+916x^325+660x^326+840x^327+360x^328+260x^329+1764x^330+920x^331+860x^332+200x^333+360x^334+1288x^335+700x^336+720x^337+140x^338+200x^339+1244x^340+480x^341+540x^342+160x^343+100x^344+688x^345+460x^346+320x^347+60x^348+60x^349+536x^350+280x^351+220x^352+80x^353+20x^354+184x^355+4x^365

The gray image is a linear code over GF(5) with n=420, k=6 and d=325.
This code was found by Heurico 1.16 in 0.566 seconds.