The generator matrix

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

generates a code of length 76 over Z7[X]/(X^2) who´s minimum homogenous weight is 440.

Homogenous weight enumerator: w(x)=1x^0+2352x^440+3654x^441+252x^442+882x^443+1008x^444+2856x^445+1470x^446+8148x^447+8796x^448+1848x^449+2016x^450+2604x^451+4158x^452+1890x^453+8778x^454+10350x^455+1722x^456+2730x^457+2352x^458+3696x^459+1512x^460+8568x^461+11634x^462+2352x^463+2604x^464+2268x^465+3696x^466+1302x^467+7140x^468+4938x^469+24x^476+18x^483+30x^490

The gray image is a linear code over GF(7) with n=532, k=6 and d=440.
This code was found by Heurico 1.16 in 6.14 seconds.