The generator matrix

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

generates a code of length 70 over Z5[X]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+880x^264+732x^265+800x^266+360x^267+800x^268+4100x^269+2236x^270+2020x^271+840x^272+1120x^273+7060x^274+3344x^275+3660x^276+1120x^277+1800x^278+7660x^279+3368x^280+3580x^281+1200x^282+2280x^283+7860x^284+2844x^285+3100x^286+1080x^287+1060x^288+5280x^289+2244x^290+1520x^291+400x^292+440x^293+2160x^294+780x^295+320x^296+20x^300+32x^305+16x^310+4x^315+4x^320

The gray image is a linear code over GF(5) with n=350, k=7 and d=264.
This code was found by Heurico 1.16 in 10.5 seconds.