The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+112x^31+440x^32+622x^33+1190x^34+1148x^35+1846x^36+1760x^37+2150x^38+1650x^39+2170x^40+1158x^41+1004x^42+560x^43+294x^44+132x^45+102x^46+18x^47+17x^48+8x^49+2x^50

The gray image is a linear code over GF(2) with n=152, k=14 and d=62.
This code was found by Heurico 1.13 in 1.92 seconds.