The generator matrix

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

generates a code of length 97 over Z5[X]/(X^2) who´s minimum homogenous weight is 370.

Homogenous weight enumerator: w(x)=1x^0+940x^370+440x^371+1160x^374+5388x^375+1540x^376+2040x^379+9724x^380+2300x^381+2520x^384+9476x^385+2220x^386+2560x^389+10680x^390+2540x^391+1940x^394+9076x^395+1860x^396+1360x^399+5360x^400+1020x^401+760x^404+2116x^405+520x^406+160x^409+332x^410+60x^411+8x^415+12x^420+4x^425+8x^430

The gray image is a linear code over GF(5) with n=485, k=7 and d=370.
This code was found by Heurico 1.16 in 16.5 seconds.