The generator matrix

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

generates a code of length 35 over Z7[X]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+2238x^196+126x^198+1344x^199+2646x^200+4410x^201+2940x^202+8136x^203+1512x^205+7014x^206+7644x^207+7350x^208+2940x^209+10356x^210+4536x^212+14280x^213+12348x^214+10878x^215+4410x^216+12456x^217+66x^224+18x^231

The gray image is a linear code over GF(7) with n=245, k=6 and d=196.
This code was found by Heurico 1.16 in 2.95 seconds.