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.