The generator matrix

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

generates a code of length 44 over Z7[X]/(X^2) who´s minimum homogenous weight is 250.

Homogenous weight enumerator: w(x)=1x^0+2940x^250+2688x^251+78x^252+588x^253+756x^254+2814x^255+1764x^256+12432x^257+7014x^258+144x^259+3234x^260+2016x^261+4662x^262+1764x^263+19824x^264+8484x^265+18x^266+6468x^267+3402x^268+6930x^269+2646x^270+18312x^271+8568x^272+42x^273+18x^280+30x^287+12x^308

The gray image is a linear code over GF(7) with n=308, k=6 and d=250.
This code was found by Heurico 1.16 in 2.98 seconds.