The generator matrix

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

generates a code of length 28 over Z7[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+120x^147+252x^150+168x^151+756x^153+456x^154+4536x^157+1260x^158+2142x^160+480x^161+27216x^164+5208x^165+5796x^167+468x^168+54432x^171+7770x^172+5712x^174+294x^175+294x^182+258x^189+30x^196

The gray image is a linear code over GF(7) with n=196, k=6 and d=147.
This code was found by Heurico 1.16 in 2.12 seconds.