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

generates a code of length 98 over Z5[X]/(X^2) who´s minimum homogenous weight is 370.

Homogenous weight enumerator: w(x)=1x^0+300x^370+448x^375+20x^376+420x^380+320x^381+420x^385+1920x^386+324x^390+5120x^391+248x^395+5120x^396+200x^400+136x^405+148x^410+124x^415+112x^420+80x^425+36x^430+48x^435+32x^440+16x^445+16x^450+8x^455+4x^460+4x^470

The gray image is a linear code over GF(5) with n=490, k=6 and d=370.
This code was found by Heurico 1.16 in 16.3 seconds.