The generator matrix

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

generates a code of length 66 over Z5[X]/(X^2) who´s minimum homogenous weight is 258.

Homogenous weight enumerator: w(x)=1x^0+240x^258+200x^259+900x^260+520x^263+100x^264+376x^265+120x^268+200x^269+92x^270+40x^273+252x^275+80x^278+4x^305

The gray image is a linear code over GF(5) with n=330, k=5 and d=258.
This code was found by Heurico 1.16 in 0.237 seconds.