The generator matrix

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

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 370.

Homogenous weight enumerator: w(x)=1x^0+444x^370+260x^372+440x^373+2348x^375+540x^377+580x^378+2160x^380+460x^382+560x^383+1972x^385+580x^387+340x^388+2128x^390+500x^392+220x^393+1052x^395+160x^397+260x^398+332x^400+100x^403+136x^405+20x^410+8x^415+4x^420+4x^425+4x^430+8x^435+4x^440

The gray image is a linear code over GF(5) with n=480, k=6 and d=370.
This code was found by Heurico 1.16 in 0.84 seconds.