The generator matrix

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

generates a code of length 52 over Z7[X]/(X^2) who´s minimum homogenous weight is 273.

Homogenous weight enumerator: w(x)=1x^0+96x^273+756x^280+1422x^287+42x^288+1716x^294+1008x^295+1872x^301+9072x^302+2076x^308+36288x^309+2316x^315+54432x^316+2502x^322+1956x^329+1236x^336+600x^343+216x^350+42x^357

The gray image is a linear code over GF(7) with n=364, k=6 and d=273.
This code was found by Heurico 1.16 in 11 seconds.