The generator matrix

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

generates a code of length 69 over Z5[X]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+1180x^256+2400x^257+1060x^258+860x^259+2136x^260+5440x^261+8240x^262+4200x^263+2740x^264+4948x^265+11720x^266+17140x^267+6660x^268+5760x^269+9088x^270+20960x^271+27660x^272+9780x^273+9280x^274+12904x^275+28360x^276+33240x^277+13300x^278+10100x^279+13984x^280+27180x^281+31420x^282+10460x^283+7560x^284+8284x^285+14720x^286+14860x^287+4140x^288+1200x^289+1712x^290+2940x^291+2540x^292+400x^293+20x^295+20x^300+16x^305+12x^320

The gray image is a linear code over GF(5) with n=345, k=8 and d=256.
This code was found by Heurico 1.16 in 294 seconds.