The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 307.

Homogenous weight enumerator: w(x)=1x^0+440x^307+800x^308+168x^310+1660x^312+1460x^313+200x^315+1680x^317+1680x^318+68x^320+1260x^322+1600x^323+44x^325+1740x^327+1420x^328+56x^330+580x^332+540x^333+40x^335+140x^337+12x^340+8x^345+4x^355+12x^360+8x^365+4x^370

The gray image is a linear code over GF(5) with n=400, k=6 and d=307.
This code was found by Heurico 1.16 in 54.2 seconds.