The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+160x^53+120x^54+8x^55+240x^58+80x^59+16x^60

The gray image is a linear code over GF(5) with n=70, k=4 and d=53.
This code was found by Heurico 1.16 in 0.000388 seconds.