The generator matrix

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

generates a code of length 15 over Z5[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+900x^53+1200x^54+40x^55+500x^56+2700x^58+1600x^59+560x^60+2000x^61+3900x^63+2200x^64+20x^70+4x^75

The gray image is a linear code over GF(5) with n=75, k=6 and d=53.
This code was found by Heurico 1.16 in 0.0568 seconds.