The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+220x^44+688x^45+200x^46+500x^48+2640x^49+3108x^50+400x^51+2000x^52+4000x^53+10560x^54+8384x^55+6100x^56+8000x^57+8000x^58+14080x^59+8304x^60+800x^61+104x^65+36x^70

The gray image is a linear code over GF(5) with n=70, k=7 and d=44.
This code was found by Heurico 1.16 in 1.31 seconds.