The generator matrix

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

generates a code of length 48 over Z5[X]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+600x^182+1060x^183+420x^184+40x^185+620x^186+1160x^187+2100x^188+500x^189+36x^190+740x^191+1080x^192+1620x^193+540x^194+16x^195+260x^196+960x^197+1620x^198+540x^199+380x^201+700x^202+600x^203+16x^205+16x^210

The gray image is a linear code over GF(5) with n=240, k=6 and d=182.
This code was found by Heurico 1.16 in 0.267 seconds.