The generator matrix

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

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+116x^300+360x^305+500x^310+100x^312+372x^315+1200x^317+360x^320+4800x^322+280x^325+6400x^327+276x^330+216x^335+160x^340+144x^345+96x^350+76x^355+64x^360+64x^365+16x^370+12x^375+8x^380+4x^390

The gray image is a linear code over GF(5) with n=405, k=6 and d=300.
This code was found by Heurico 1.16 in 1.46 seconds.