The generator matrix

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

generates a code of length 48 over Z5[X]/(X^2) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+440x^177+760x^178+440x^179+912x^180+1520x^181+1860x^182+2880x^183+1420x^184+2916x^185+2940x^186+3640x^187+4040x^188+2300x^189+3844x^190+3660x^191+5020x^192+6000x^193+3580x^194+5148x^195+4780x^196+4400x^197+4560x^198+2060x^199+2712x^200+2100x^201+2140x^202+1760x^203+200x^204+20x^205+16x^210+32x^215+8x^220+8x^225+4x^230+4x^235

The gray image is a linear code over GF(5) with n=240, k=7 and d=177.
This code was found by Heurico 1.16 in 12.1 seconds.