The generator matrix

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

generates a code of length 15 over Z5[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+360x^54+48x^55+300x^56+480x^59+36x^60+1200x^61+660x^64+24x^65+12x^70+4x^75

The gray image is a linear code over GF(5) with n=75, k=5 and d=54.
This code was found by Heurico 1.16 in 0.00408 seconds.