The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  X  0 X^2+X X^2  1  1  1 X^2+X X^2+X  1  1  0  1  X X^2+X  1 X^2  X X^2 X^2+X  1  1 X^2+X  X  1  X  1
 0  1  0  0  0  1 X^2+X+1  1 X+1  0  X  1  1  1  X X+1 X^2  X X^2+X  X  1 X^2+X X^2 X^2+X  1  0 X+1  1 X^2+X X^2+X  1  X X^2 X^2+X  1 X+1 X^2+X  0
 0  0  1  0  1  1  X  0 X^2+1  X  1 X^2+1 X^2+1  0  1  X X^2 X^2+X  1  X X^2 X^2+X+1  1 X+1  0  1 X+1 X+1  1  0  1 X^2 X^2+X+1  1  X  X  1  0
 0  0  0  1  1  0 X^2  1 X^2+1 X^2+1  0 X^2+1  0 X^2+1 X^2+X+1 X+1  X X+1 X^2+X  1  0 X^2  1 X^2+X+1 X^2+X  X X^2+X X^2+1 X^2+X+1  1 X^2  0  1  1  1 X+1  X  0
 0  0  0  0  X  0  0 X^2  0 X^2 X^2  0  X X^2+X  X  X X^2+X X^2+X X^2  X X^2+X  X X^2 X^2 X^2+X X^2+X X^2  0  X  0 X^2  X X^2+X  0  0  0  X X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 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+106x^30+358x^31+752x^32+1204x^33+2051x^34+2476x^35+3520x^36+3558x^37+4431x^38+3796x^39+3774x^40+2490x^41+1991x^42+1116x^43+602x^44+298x^45+151x^46+62x^47+21x^48+2x^49+6x^50+2x^52

The gray image is a linear code over GF(2) with n=152, k=15 and d=60.
This code was found by Heurico 1.16 in 19.7 seconds.