The generator matrix

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

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+216x^45+400x^48+408x^50+500x^52+4800x^53+440x^55+2500x^56+4000x^57+19200x^58+760x^60+10000x^61+8000x^62+25600x^63+780x^65+424x^70+96x^75

The gray image is a linear code over GF(5) with n=75, k=7 and d=45.
This code was found by Heurico 1.16 in 1.57 seconds.