The generator matrix

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

generates a code of length 14 over Z5[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+220x^41+600x^44+3312x^45+2720x^46+3000x^48+7200x^49+15044x^50+8520x^51+15000x^52+24000x^53+28800x^54+42640x^55+36420x^56+60000x^57+48000x^58+38400x^59+41980x^60+14620x^61+120x^65+28x^70

The gray image is a linear code over GF(5) with n=70, k=8 and d=41.
This code was found by Heurico 1.16 in 29.5 seconds.