The generator matrix

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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 310.

Homogenous weight enumerator: w(x)=1x^0+272x^310+660x^313+520x^314+1556x^315+1360x^318+600x^319+1892x^320+780x^323+420x^324+1592x^325+1000x^328+440x^329+1768x^330+920x^333+360x^334+820x^335+280x^338+160x^339+176x^340+8x^345+8x^350+8x^355+8x^360+8x^365+4x^375+4x^380

The gray image is a linear code over GF(5) with n=405, k=6 and d=310.
This code was found by Heurico 1.16 in 0.652 seconds.