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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+70x^28+128x^29+344x^30+810x^31+1168x^32+1822x^33+2509x^34+3324x^35+4023x^36+4150x^37+4258x^38+3416x^39+2511x^40+1930x^41+1067x^42+612x^43+307x^44+162x^45+106x^46+30x^47+16x^48+3x^50+1x^58

The gray image is a linear code over GF(2) with n=148, k=15 and d=56.
This code was found by Heurico 1.16 in 20 seconds.