The generator matrix

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

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+58x^30+174x^31+444x^32+748x^33+1241x^34+1908x^35+2594x^36+3154x^37+3874x^38+4344x^39+3824x^40+3318x^41+2634x^42+1856x^43+1234x^44+686x^45+372x^46+162x^47+91x^48+30x^49+12x^50+4x^51+4x^52+1x^66

The gray image is a linear code over GF(2) with n=156, k=15 and d=60.
This code was found by Heurico 1.16 in 22 seconds.