The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1  1  1  X  X  0  1 X^2  X  0  1  1  1  1  1  1  X  1 X^2+X  X  1  X  1  1 X^2+X X^2+X  1
 0  1  0  0  0  0 X+1  X X^2 X+1  1 X^2 X^2+1 X+1 X^2+X+1  1  1  1  0  1  1  X  X X^2+1 X^2  0 X^2+1 X^2+1 X^2 X+1  X X^2+X X^2+1  1 X^2+X  X  0 X^2+X X^2
 0  0  1  0  0  0  1 X+1  1 X^2+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X X+1 X^2+X  1 X^2 X^2+X+1 X^2+1 X^2+X  1 X^2+X X^2+1 X+1 X^2+1 X^2+X+1  1 X^2+X  1  1  1 X^2+X X+1  X  0  1  0
 0  0  0  1  0  1 X^2 X^2+1  1 X+1 X^2+1 X^2+X X^2 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+X+1 X^2+X X^2  0  1 X^2+1  1 X^2+X X^2+X  0 X^2+1 X+1 X^2+1 X^2+1  0 X^2+X+1  0  1 X^2+X+1  1  1  X
 0  0  0  0  1  1 X^2+1  X X+1 X^2+1 X^2+X X^2+1  0 X^2 X^2+X+1  0 X^2+1 X^2+1 X^2+1 X^2+X+1 X^2 X^2+1 X+1  0  X X+1  X  X X^2+X X^2+1 X^2+1 X^2+1 X+1 X+1 X^2 X^2 X^2+1  0  X
 0  0  0  0  0  X  0  X  X X^2+X  X X^2  0  X X^2+X  X X^2  X  0 X^2 X^2 X^2+X  0 X^2 X^2+X X^2+X  X  0 X^2  0 X^2  X  0 X^2+X X^2+X  0 X^2+X X^2+X  X

generates a code of length 39 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+156x^30+748x^31+1565x^32+2910x^33+4727x^34+7484x^35+10255x^36+13030x^37+15779x^38+16654x^39+16263x^40+13938x^41+10828x^42+7450x^43+4331x^44+2566x^45+1322x^46+614x^47+251x^48+128x^49+49x^50+10x^51+6x^52+4x^53+3x^54

The gray image is a linear code over GF(2) with n=156, k=17 and d=60.
This code was found by Heurico 1.13 in 104 seconds.