The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 304.

Homogenous weight enumerator: w(x)=1x^0+1080x^304+1220x^305+1760x^306+320x^308+3680x^309+3136x^310+3700x^311+580x^313+5600x^314+4912x^315+4220x^316+480x^318+6280x^319+4788x^320+4980x^321+440x^323+6580x^324+4544x^325+4140x^326+400x^328+4900x^329+3400x^330+2840x^331+140x^333+1700x^334+1052x^335+860x^336+140x^338+180x^339+24x^340+8x^345+16x^350+16x^355+8x^360

The gray image is a linear code over GF(5) with n=400, k=7 and d=304.
This code was found by Heurico 1.16 in 279 seconds.