The generator matrix

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

generates a code of length 12 over Z5[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+960x^37+1092x^40+4320x^42+3000x^44+7312x^45+12480x^47+10000x^48+12000x^49+14496x^50+12240x^52+192x^55+32x^60

The gray image is a linear code over GF(5) with n=60, k=7 and d=37.
This code was found by Heurico 1.16 in 9.57 seconds.