The generator matrix

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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+462x^153+36x^154+378x^156+1008x^157+2982x^158+7812x^159+2562x^160+114x^161+882x^162+4536x^163+5040x^164+8148x^165+12306x^166+4074x^167+72x^168+5292x^169+13608x^170+10416x^171+13566x^172+18984x^173+5250x^174+48x^175+54x^182+18x^189

The gray image is a linear code over GF(7) with n=196, k=6 and d=153.
This code was found by Heurico 1.16 in 1.88 seconds.