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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 307.

Homogenous weight enumerator: w(x)=1x^0+600x^307+880x^308+480x^309+608x^310+1380x^311+2980x^312+2640x^313+900x^314+1212x^315+2760x^316+3940x^317+4380x^318+1460x^319+1732x^320+3220x^321+5800x^322+4660x^323+1620x^324+1860x^325+2920x^326+4760x^327+4880x^328+1680x^329+1476x^330+3020x^331+4320x^332+3420x^333+1060x^334+928x^335+1240x^336+2100x^337+1480x^338+300x^339+244x^340+460x^341+500x^342+160x^343+28x^345+8x^350+8x^355+8x^360+8x^365+4x^370

The gray image is a linear code over GF(5) with n=405, k=7 and d=307.
This code was found by Heurico 1.16 in 13.4 seconds.