The generator matrix

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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+120x^225+20x^228+80x^229+624x^230+240x^232+1340x^233+640x^234+1180x^235+1040x^237+3860x^238+1500x^239+1996x^240+1840x^242+6260x^243+2400x^244+3172x^245+3840x^247+11860x^248+3700x^249+4048x^250+3940x^252+10240x^253+3220x^254+2848x^255+1600x^257+3920x^258+960x^259+1044x^260+200x^265+128x^270+116x^275+88x^280+36x^285+24x^290

The gray image is a linear code over GF(5) with n=310, k=7 and d=225.
This code was found by Heurico 1.16 in 11.8 seconds.