The generator matrix

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

generates a code of length 15 over Z5[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+312x^50+500x^52+556x^55+4000x^57+1216x^60+8000x^62+916x^65+96x^70+28x^75

The gray image is a linear code over GF(5) with n=75, k=6 and d=50.
This code was found by Heurico 1.16 in 0.071 seconds.