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  3  1  3  1  0  1  1  1  1  1  3  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  0  1  3  1  1  3  1  1  1  1  1  1
 0  3 24  0 21 24  0 21 24  9 21 24  6  0 21 12  6  9 24  0 21 12  0 24  9  3  6 15  9 24  0 21 18  3 24 12  9 21 21 15 24 15  3 18  9 21 21 15 21  9  9 12  3 24 21 18  9  9 12 18  3 24 24 21  3  3 21 15  9 24 21 12  6 18  0  0
 0  0  9  0  0  0  0 18  9  0  9 18 18  0  0  9  0  0  9 18 18  9  9 18 18  9  0 18 18  9 18 18 18 18 18 18  9 18  9  0 18  0 18 18  0  0  0  0  9 18 18 18 18  0  0 18 18  0  0  9 18  9 18  0  0  9 18  0  0  0 18  0  9  9  9  0
 0  0  0  9  0  0  0  0  0 18  0  9 18  9  9  9  9 18  9 18  9  9  0 18  9  0  9  9 18 18  9 18  0  9  0 18  9  9  0 18 18  0  0 18 18  0 18 18  0  0 18 18  0  9 18  0  0  9 18  0  9  0 18 18  0  9  0 18  9  9  9 18 18  9  0  0
 0  0  0  0 18  0  9 18  9  9  0  9 18  0 18  0 18  0 18 18  0  0 18  9  9  0  0 18 18 18  0 18 18 18  0  9 18  0  9 18 18 18  9  9 18  9 18  0 18  0 18  0  9  0  9  0  9 18  0  0 18 18 18  0  9 18 18 18 18  9 18 18  9  0  9  0
 0  0  0  0  0  9  9  0 18  9  0  0  9  9 18 18  9  9  0 18  0  0 18  9  9  9  9  0  9  0  9 18  0  9  9  9  0  9 18  9  0  0 18 18 18  9 18 18 18  0  0  9  0 18  0 18  9  9  0 18  0 18  0 18  9 18  0  0 18 18 18  0  0  0 18  0

generates a code of length 76 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+68x^138+78x^140+294x^141+24x^142+180x^143+478x^144+120x^145+492x^146+516x^147+732x^148+2166x^149+462x^150+2304x^151+4086x^152+484x^153+2364x^154+2760x^155+436x^156+240x^157+204x^158+420x^159+48x^160+162x^161+248x^162+42x^164+128x^165+36x^167+38x^168+32x^171+14x^174+6x^177+8x^180+4x^183+2x^186+4x^192+2x^204

The gray image is a code over GF(3) with n=684, k=9 and d=414.
This code was found by Heurico 1.16 in 2.93 seconds.