The generator matrix

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

generates a code of length 48 over Z5[X]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+120x^170+40x^171+40x^174+568x^175+180x^176+480x^177+260x^178+440x^179+1728x^180+940x^181+1160x^182+960x^183+1340x^184+4196x^185+2040x^186+2360x^187+3060x^188+3440x^189+7152x^190+3840x^191+3660x^192+4960x^193+4640x^194+9224x^195+3800x^196+3560x^197+3260x^198+2600x^199+4376x^200+1660x^201+1280x^202+304x^205+204x^210+148x^215+56x^220+40x^225+8x^230

The gray image is a linear code over GF(5) with n=240, k=7 and d=170.
This code was found by Heurico 1.16 in 8.53 seconds.