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

generates a code of length 96 over Z5[X]/(X^2) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+168x^360+376x^365+444x^370+100x^372+464x^375+1200x^377+296x^380+4800x^382+288x^385+6400x^387+232x^390+188x^395+128x^400+140x^405+128x^410+60x^415+80x^420+68x^425+20x^430+16x^435+8x^440+8x^445+4x^450+4x^455+4x^465

The gray image is a linear code over GF(5) with n=480, k=6 and d=360.
This code was found by Heurico 1.16 in 1.82 seconds.