The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 303.

Homogenous weight enumerator: w(x)=1x^0+920x^303+560x^304+440x^305+420x^306+320x^307+4780x^308+2280x^309+1072x^310+800x^311+940x^312+7420x^313+3300x^314+1912x^315+900x^316+1040x^317+8620x^318+3980x^319+1500x^320+1000x^321+1240x^322+9360x^323+3240x^324+1616x^325+1200x^326+1040x^327+7480x^328+2740x^329+1100x^330+480x^331+420x^332+3260x^333+1280x^334+412x^335+200x^336+660x^338+120x^339+32x^340+4x^345+12x^350+24x^355

The gray image is a linear code over GF(5) with n=400, k=7 and d=303.
This code was found by Heurico 1.16 in 13.1 seconds.