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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+90x^150+18x^151+108x^153+102x^154+112x^156+222x^157+100x^159+294x^160+68x^162+360x^163+62x^165+318x^166+32x^168+120x^169+38x^171+24x^172+22x^174+30x^177+10x^180+14x^183+12x^186+12x^189+4x^192+4x^195+4x^198+2x^201+2x^207+2x^213

The gray image is a linear code over GF(3) with n=243, k=7 and d=150.
This code was found by Heurico 1.16 in 0.264 seconds.