The generator matrix

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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 300.

Homogenous weight enumerator: w(x)=1x^0+136x^300+100x^303+140x^304+660x^305+1140x^308+640x^309+2996x^310+2400x^313+1580x^314+4772x^315+3820x^318+2200x^319+7192x^320+6220x^323+2600x^324+11132x^325+6220x^328+3160x^329+8932x^330+4080x^333+1860x^334+3764x^335+1020x^338+320x^339+504x^340+152x^345+140x^350+108x^355+80x^360+24x^365+16x^370+16x^375

The gray image is a linear code over GF(5) with n=405, k=7 and d=300.
This code was found by Heurico 1.16 in 14.9 seconds.