The generator matrix

 1  0  0  1  1  1  1  1  1 2X  0  1  X  1  1  1  1  1  1  X  1  1  X  1  1  X  1  1  X  1  1  1  0  1  1  1  X  1  0  1  1  1  X  1  1  1  1  1 2X  1 2X  1  1  0 2X  1 2X  1  1  0  0  1  1  X 2X  1  1  0  1  1  1  0  1  1  1  1  X  1  X  1  1  1  1  1 2X  1  1  1
 0  1  0  0  X 2X+1  1  2 2X+1  1  1  2 2X 2X+1  1  1 X+2 2X+2  X  1  X 2X+2  1  1 2X  1  0  1  0 X+2 2X+2 2X+1  1  2 2X X+1  1 X+2  1 2X+2 X+1 X+2  X 2X+1 X+1 2X 2X+2 X+1  1 X+1  1  0 2X+1  1  1  2  1  1  X  1  0  2 2X  1  1 2X  0 2X  2 2X X+2  0  X 2X X+2  1  1 X+1  1 2X+2 X+2  2  0 2X+1  1  2 2X+1  X
 0  0  1  1 2X+2 X+2 X+1  0 2X 2X+1 2X+2  X  1  2  1 2X 2X+1  2  X  0 X+2 X+1 X+2  1 2X+1 2X+1 X+1 X+2  1 2X+2 2X 2X  X 2X+1 2X+2 2X+2 X+2  0  1 X+2 2X+1 2X+2  1 X+2 2X+1 2X X+1  X X+2 X+1 X+1 X+2  X 2X  0 X+1 2X+1 X+1  0  X  1 2X+2 X+1 2X+2  2  0  1  1  0 2X+1 X+2  1 X+2 X+1 2X+1  0  X 2X+2 2X 2X+2  2 2X+1 X+1  X 2X+2 X+2 2X+1  X
 0  0  0 2X 2X 2X 2X 2X  X 2X 2X  X 2X  0  X  0  X 2X 2X 2X  0 2X  0  0 2X  0  0  X  X  X  X  0  0  0  X  0 2X 2X 2X  0 2X 2X  X  X  X  0  X 2X  X  0  0  0  0  X 2X  X  X  X  0  X  X  0 2X  X  0  X  X  0  0  0  0 2X  X  X  0 2X  X  X 2X 2X  X  X  X  X  X  X  X  0

generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+130x^168+84x^169+144x^170+324x^171+108x^172+126x^173+252x^174+126x^175+102x^176+206x^177+66x^178+18x^179+40x^180+18x^181+24x^182+76x^183+30x^184+6x^185+72x^186+42x^187+36x^188+52x^189+6x^191+50x^192+6x^193+18x^194+6x^195+6x^196+6x^198+6x^200

The gray image is a linear code over GF(3) with n=264, k=7 and d=168.
This code was found by Heurico 1.16 in 0.21 seconds.