The generator matrix

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

generates a code of length 74 over Z5[X]/(X^2) who´s minimum homogenous weight is 284.

Homogenous weight enumerator: w(x)=1x^0+1320x^284+480x^285+2680x^289+824x^290+2300x^294+492x^295+2820x^299+592x^300+2640x^304+540x^305+740x^309+148x^310+8x^315+8x^325+12x^330+8x^335+4x^340+4x^345+4x^355

The gray image is a linear code over GF(5) with n=370, k=6 and d=284.
This code was found by Heurico 1.16 in 2.84 seconds.