The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+120x^29+350x^30+726x^31+1124x^32+1982x^33+2432x^34+3542x^35+3696x^36+4498x^37+3919x^38+3850x^39+2437x^40+1958x^41+1055x^42+562x^43+283x^44+142x^45+47x^46+24x^47+10x^48+4x^49+5x^50+1x^52

The gray image is a linear code over GF(2) with n=148, k=15 and d=58.
This code was found by Heurico 1.16 in 20.2 seconds.