The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+80x^48+1020x^49+744x^50+100x^52+640x^53+3060x^54+1028x^55+1500x^56+400x^57+1280x^58+4420x^59+1336x^60+4x^65+12x^70

The gray image is a linear code over GF(5) with n=70, k=6 and d=48.
This code was found by Heurico 1.16 in 0.0473 seconds.