The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X 1
0 X 0 0 X X 0 X 2X 4X 3X X 0
0 0 X 0 3X 2X X 4X 0 X X 3X 0
0 0 0 X 3X X 4X 3X 3X 3X 0 X 0
generates a code of length 13 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+64x^40+156x^45+500x^48+100x^50+2000x^53+96x^55+176x^60+32x^65
The gray image is a linear code over GF(5) with n=65, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00567 seconds.