The generator matrix

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

generates a code of length 12 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+192x^40+500x^44+112x^45+2000x^49+96x^50+192x^55+32x^60

The gray image is a linear code over GF(5) with n=60, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00453 seconds.