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

generates a code of length 87 over Z5[X]/(X^2) who´s minimum homogenous weight is 336.

Homogenous weight enumerator: w(x)=1x^0+140x^336+268x^340+440x^341+132x^345+640x^346+80x^350+840x^351+68x^355+440x^356+32x^365+4x^370+4x^375+8x^380+20x^390+4x^395+4x^405

The gray image is a linear code over GF(5) with n=435, k=5 and d=336.
This code was found by Heurico 1.16 in 65.2 seconds.