The generator matrix

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

generates a code of length 46 over Z5[X]/(X^2) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+820x^174+416x^175+360x^176+360x^177+300x^178+2400x^179+1056x^180+660x^181+480x^182+360x^183+1860x^184+648x^185+400x^186+360x^187+180x^188+1800x^189+732x^190+580x^191+300x^192+160x^193+1120x^194+256x^195+8x^200+8x^205

The gray image is a linear code over GF(5) with n=230, k=6 and d=174.
This code was found by Heurico 1.16 in 0.262 seconds.