The generator matrix

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

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+292x^275+456x^280+100x^284+464x^285+1200x^289+364x^290+4800x^294+308x^295+6400x^299+244x^300+236x^305+200x^310+136x^315+180x^320+88x^325+84x^330+36x^335+20x^340+12x^345+4x^355

The gray image is a linear code over GF(5) with n=370, k=6 and d=275.
This code was found by Heurico 1.16 in 14 seconds.