The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+276x^38+372x^39+1162x^40+1344x^41+2285x^42+2268x^43+3374x^44+3192x^45+4143x^46+3100x^47+3685x^48+2512x^49+2178x^50+1124x^51+920x^52+376x^53+314x^54+48x^55+72x^56+17x^58+2x^60+3x^62

The gray image is a linear code over GF(2) with n=184, k=15 and d=76.
This code was found by Heurico 1.16 in 26.4 seconds.