The generator matrix

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

generates a code of length 38 over Z7[X]/(X^2) who´s minimum homogenous weight is 214.

Homogenous weight enumerator: w(x)=1x^0+2982x^214+126x^216+1104x^217+1974x^218+3654x^219+3486x^220+11634x^221+1512x^223+5160x^224+5460x^225+5922x^226+3612x^227+15120x^228+4536x^230+10428x^231+9030x^232+8946x^233+5250x^234+17598x^235+48x^238+48x^245+18x^252

The gray image is a linear code over GF(7) with n=266, k=6 and d=214.
This code was found by Heurico 1.16 in 16.5 seconds.