The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X 3X  1  1  1 5X  1  1
 0  1  0 5X 3X 6X  1 5X+3  2 X+1 5X+1 4X+1 5X+2  6 X+6 4X+2 5X+5 5X+6 4X+4  1  1 6X+5 2X+5 2X+4  1 X+4  5
 0  0  1 5X+1  3 5X+2  2 6X+2 4X+2 5X+4 5X X+5 5X+5 X+3 5X+6 3X+6 2X+4 6X+1 6X+6 X+6 6X+1 3X+3 2X+1 6X+3 X+3 3X+1  5

generates a code of length 27 over Z7[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+294x^150+756x^151+5292x^152+8400x^153+120x^154+3528x^157+3780x^158+14112x^159+12600x^160+126x^161+6174x^162+10584x^164+7812x^165+23814x^166+20160x^167+36x^168+42x^175+18x^189

The gray image is a linear code over GF(7) with n=189, k=6 and d=150.
This code was found by Heurico 1.16 in 7.34 seconds.