The generator matrix

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

generates a code of length 61 over Z5[X]/(X^2) who´s minimum homogenous weight is 241.

Homogenous weight enumerator: w(x)=1x^0+40x^241+80x^243+400x^244+4x^245+60x^246+20x^248+16x^255+4x^260

The gray image is a linear code over GF(5) with n=305, k=4 and d=241.
This code was found by Heurico 1.16 in 0.0277 seconds.