The generator matrix

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

generates a code of length 84 over Z5[X]/(X^2) who´s minimum homogenous weight is 330.

Homogenous weight enumerator: w(x)=1x^0+780x^330+1576x^335+340x^340+160x^345+264x^350+4x^360

The gray image is a linear code over GF(5) with n=420, k=5 and d=330.
This code was found by Heurico 1.16 in 0.109 seconds.