The generator matrix

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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 274.

Homogenous weight enumerator: w(x)=1x^0+240x^274+432x^275+560x^276+520x^279+336x^280+240x^281+120x^284+280x^285+40x^286+40x^289+44x^290+160x^291+80x^294+28x^295+4x^325

The gray image is a linear code over GF(5) with n=350, k=5 and d=274.
This code was found by Heurico 1.16 in 1.74 seconds.