The generator matrix

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

generates a code of length 15 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+304x^40+812x^45+1436x^50+2760x^55+12500x^56+4140x^60+50000x^61+3616x^65+1988x^70+568x^75

The gray image is a linear code over GF(5) with n=75, k=7 and d=40.
This code was found by Heurico 1.16 in 2.76 seconds.