The generator matrix

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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+46x^30+30x^31+139x^32+200x^33+308x^34+398x^35+551x^36+898x^37+1171x^38+1542x^39+1903x^40+1952x^41+1832x^42+1676x^43+1211x^44+932x^45+601x^46+394x^47+235x^48+104x^49+116x^50+54x^51+45x^52+10x^53+21x^54+2x^55+9x^56+1x^60+1x^62+1x^64

The gray image is a linear code over GF(2) with n=164, k=14 and d=60.
This code was found by Heurico 1.16 in 10.3 seconds.