The generator matrix

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

generates a code of length 47 over Z5[X]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+1328x^170+1400x^171+1180x^172+1580x^173+2640x^174+6272x^175+5580x^176+4620x^177+4600x^178+6600x^179+14676x^180+13540x^181+11000x^182+10220x^183+14340x^184+28488x^185+23340x^186+19080x^187+16440x^188+21980x^189+37516x^190+28740x^191+21460x^192+15160x^193+16420x^194+25036x^195+16040x^196+7660x^197+4500x^198+3020x^199+4736x^200+1360x^201+48x^205+16x^210+8x^215

The gray image is a linear code over GF(5) with n=235, k=8 and d=170.
This code was found by Heurico 1.16 in 157 seconds.