The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+28x^29+183x^30+372x^31+731x^32+1224x^33+1854x^34+2436x^35+3403x^36+4088x^37+3924x^38+4168x^39+3667x^40+2564x^41+1720x^42+1092x^43+708x^44+340x^45+153x^46+60x^47+33x^48+12x^49+6x^50+1x^60

The gray image is a linear code over GF(2) with n=152, k=15 and d=58.
This code was found by Heurico 1.16 in 21.4 seconds.