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  3  1  3  1  1  3  1  1  1  3  1  1  1  1  1  1  1  1  3  3  3  1  1
 0  9  0  0  0  0  0  0  0  0  9 18 18  9  9  9  0 18  9 18  9  0  9  0 18  9  0 18  9 18 18 18  9  9  9  0 18 18  0  0  0  9 18  9  9  9  0 18  9 18  9  9  0 18  0 18 18  9 18  9  0  0 18 18 18  9 18  0 18 18  0  9 18  0  0
 0  0  9  0  0  0  0  9 18 18 18  0  0 18  9 18  9  0  9  9  0 18 18  0  9  9 18  0  9  0 18 18 18  9 18  0 18 18  9  9 18 18 18 18  0 18  0 18  0  9  9  0  0  0  9  0  0  9 18  9 18  9  0 18  9  0  9  9  0  9  0 18  0  9  0
 0  0  0  9  0  0  9 18  0 18  0  0 18  9  9 18  0  9  0 18  0 18 18  0 18  0  9 18 18  9  9  9 18  0  0 18 18  9  0 18  9 18 18  9  9  9  9 18  0  0  0  0  9  0  9 18  0  0 18 18  0  0  9 18  9  9  9 18  9  9  9 18 18  0 18
 0  0  0  0  9  0 18 18  9  0 18 18 18  0 18 18  0 18  9  0 18 18  0  9 18  0 18  9  0  9  0  9  0 18  0 18  0 18 18  9  0  9 18  9  0 18 18 18  9  9  9  9  0  0 18  0  0  9  0  9  0  9  0  9 18 18 18 18  0  9 18  9  0 18 18
 0  0  0  0  0  9 18 18 18 18 18 18  9 18  9  9 18  9 18 18 18 18  0 18  0  9  0  0 18  9 18  0 18  9  0  9  9  0  0  9  0  9 18  9 18  9  9  0  9  9  9 18  9 18 18  9  0 18 18 18  9  0 18  0 18 18  0  9  9  0  9 18  0  9 18

generates a code of length 75 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+94x^138+6x^139+124x^141+66x^142+94x^144+192x^145+80x^147+342x^148+4440x^150+474x^151+48x^153+294x^154+64x^156+84x^157+48x^159+20x^162+16x^165+24x^168+26x^171+6x^174+2x^177+10x^183+4x^186+2x^204

The gray image is a code over GF(3) with n=675, k=8 and d=414.
This code was found by Heurico 1.16 in 0.695 seconds.