The generator matrix

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

generates a code of length 15 over Z5[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+208x^45+416x^50+500x^52+480x^55+4000x^57+680x^60+8000x^62+820x^65+432x^70+88x^75

The gray image is a linear code over GF(5) with n=75, k=6 and d=45.
This code was found by Heurico 1.16 in 0.151 seconds.