The generator matrix

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

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+16x^40+52x^45+500x^48+32x^50+4x^55+20x^60

The gray image is a linear code over GF(5) with n=60, k=4 and d=40.
This code was found by Heurico 1.16 in 0.000452 seconds.