The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+273x^30+716x^31+1585x^32+2508x^33+3630x^34+5120x^35+6628x^36+7760x^37+8451x^38+8248x^39+6822x^40+5576x^41+3723x^42+2208x^43+1240x^44+528x^45+324x^46+92x^47+76x^48+12x^49+15x^50

The gray image is a linear code over GF(2) with n=152, k=16 and d=60.
This code was found by Heurico 1.13 in 25.7 seconds.