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

generates a code of length 69 over Z5[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+68x^240+412x^245+812x^250+1076x^255+1300x^260+1516x^265+2500x^268+1496x^270+20000x^273+1548x^275+40000x^278+1724x^280+1540x^285+1372x^290+1116x^295+836x^300+460x^305+236x^310+84x^315+16x^320+8x^325+4x^335

The gray image is a linear code over GF(5) with n=345, k=7 and d=240.
This code was found by Heurico 1.16 in 27.8 seconds.