The generator matrix

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

generates a code of length 74 over Z5[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+56x^270+220x^274+296x^275+20x^276+80x^277+1160x^279+1044x^280+460x^281+600x^282+2700x^284+1616x^285+1200x^286+1580x^287+5700x^289+2284x^290+2200x^291+2380x^292+8600x^294+3316x^295+3800x^296+3680x^297+9980x^299+3428x^300+3580x^301+3200x^302+6940x^304+2412x^305+1240x^306+980x^307+2200x^309+628x^310+156x^315+132x^320+100x^325+60x^330+52x^335+20x^340+16x^345+4x^355+4x^360

The gray image is a linear code over GF(5) with n=370, k=7 and d=270.
This code was found by Heurico 1.16 in 13.3 seconds.