The generator matrix

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

generates a code of length 74 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+556x^275+1120x^276+1700x^277+1540x^278+1420x^279+4352x^280+5720x^281+6240x^282+4020x^283+3760x^284+9280x^285+11440x^286+11320x^287+8180x^288+5940x^289+15488x^290+18360x^291+17640x^292+10360x^293+9820x^294+22996x^295+26120x^296+22840x^297+14120x^298+11400x^299+22564x^300+24760x^301+20140x^302+11240x^303+7360x^304+15836x^305+14320x^306+10700x^307+4920x^308+2600x^309+4060x^310+3160x^311+1920x^312+620x^313+200x^314+452x^315+8x^320+12x^325+8x^335+8x^340+4x^345

The gray image is a linear code over GF(5) with n=370, k=8 and d=275.
This code was found by Heurico 1.16 in 295 seconds.