The generator matrix

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

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+96x^50+204x^55+500x^56+64x^60+2000x^61+144x^65+84x^70+32x^75

The gray image is a linear code over GF(5) with n=75, k=5 and d=50.
This code was found by Heurico 1.16 in 0.00778 seconds.