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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+348x^240+784x^245+20x^248+1032x^250+1200x^255+1200x^258+1428x^260+4800x^263+1496x^265+15600x^268+1616x^270+24480x^273+1700x^275+16400x^278+1592x^280+1476x^285+1204x^290+876x^295+432x^300+288x^305+96x^310+52x^315+4x^320

The gray image is a linear code over GF(5) with n=340, k=7 and d=240.
This code was found by Heurico 1.16 in 27.8 seconds.