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

generates a code of length 60 over Z5[X]/(X^2) who´s minimum homogenous weight is 205.

Homogenous weight enumerator: w(x)=1x^0+96x^205+376x^210+896x^215+1056x^220+100x^224+1348x^225+1600x^229+1508x^230+9600x^234+1544x^235+25600x^239+1668x^240+25600x^244+1764x^245+1624x^250+1496x^255+1072x^260+716x^265+340x^270+92x^275+20x^280+8x^285

The gray image is a linear code over GF(5) with n=300, k=7 and d=205.
This code was found by Heurico 1.16 in 23.4 seconds.