The generator matrix

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

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+124x^168+128x^171+210x^174+410x^177+536x^180+448x^183+168x^186+42x^189+20x^192+24x^195+12x^198+16x^201+20x^204+8x^207+6x^210+10x^213+2x^219+2x^252

The gray image is a linear code over GF(3) with n=270, k=7 and d=168.
This code was found by Heurico 1.16 in 1.36 seconds.