The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1 5X  1  1  1  1  1 2X  1  1  1  1  1  1  1 4X  1  1  X  1  1  1  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1 3X  1  1  1  1  1 6X  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0 5X 3X 6X  1 5X+3  2 5X+1 4X+1 6X+1  1 4X+6 5X+4 3X+6  3 5X+2 X+3 3X+4 6X+6 X+2  4  1 3X+2  X 3X+1 4X+6 4X+4  1 X+4 6X+3 4X+1 2X+2 2X+6  6 5X  1 6X 4X+3  1 6X+3 3X+4 4X+2 6X+1 3X+6  1 5X+3 5X+2 5X+4 6X+5 5X+5 3X+5  5 4X+5 3X+5 4X+5 2X+3 4X+4 3X+2 2X X+1  1 6X 2X 3X+2 3X 5X+1 6X+6 X+5  4 4X+3  1 6X+5 5X+3 5X+6  1 4X+4 4X+2 X+6 3X+1 4X+5 2X+6 2X+5 3X+3 3X+5 5X 3X+6
 0  0  1 5X+1  3 5X+2  2 6X+2 4X+2 5X+5  6 5X+3 3X+3 3X+4 3X+3 6X+3 2X+3 4X+3 4X+5 X+1 4X  1 4X+4 X+2 3X+5  4  X 4X+6 5X+6  6 2X 2X+6 5X+4 5X 3X+1 4X+2 X+6 2X+1 5X+5 6X 2X+4 6X+1 2X+5  4 6X+1 X+5 2X+5 5X+4 2X+6 6X+2 2X+4 4X+3  5 6X+6 5X+1  0 3X+2 2X+2  X 6X+4 4X+6 X+4 6X+4 3X+2 4X 2X+5  1 6X+5 6X+5  0 4X+5 6X+4 X+2 5X+6  X X+4 6X+6 4X+6 2X+6 2X+2 6X+3 6X+2  3 3X+3 X+4 5X+4 2X+3 5X+3

generates a code of length 88 over Z7[X]/(X^2) who´s minimum homogenous weight is 512.

Homogenous weight enumerator: w(x)=1x^0+2940x^512+4074x^513+3360x^514+714x^515+252x^516+1176x^517+72x^518+9828x^519+7728x^520+5922x^521+1386x^522+714x^523+1890x^524+102x^525+11046x^526+8442x^527+6510x^528+2142x^529+462x^530+1512x^531+126x^532+10752x^533+8610x^534+5166x^535+1932x^536+630x^537+1596x^538+8652x^540+6132x^541+3738x^542+18x^546+6x^553+18x^560

The gray image is a linear code over GF(7) with n=616, k=6 and d=512.
This code was found by Heurico 1.16 in 6.7 seconds.