The generator matrix

 1  0  0  1  1  1  0  1 X^2+X  1 X^2+X  1  X  1 X^2+X  1  1  1  1  1 X^3+X  1 X^3+X^2 X^2  1  1 X^3+X  1  1  1 X^3+X^2+X  1  X  1  1 X^3+X X^3+X^2+X  1  1 X^3+X^2+X  1
 0  1  0  0 X^3+X^2+1 X^2+1  1 X^3+X X^2 X^2+X+1  1 X+1  1 X^2  1 X^3+X X^3+X^2+1 X+1 X^3+X^2+X+1 X^2 X^2+X X^2+X  1 X^3+X X^3+1 X^2+X+1  1 X^3+X^2  1  0  X X^3+X+1  1 X^3+X^2+X+1 X^3+1  1  1 X^3+X+1 X^3  X X^2
 0  0  1 X+1 X+1  0 X^2+X+1 X^3+X^2+X  1 X^3+X+1 X^3  X X^2+X+1  1  X X^3+X^2 X^3+X^2+1 X^3+X^2  1 X^3+X^2+X  1 X^2+1 X^3  1 X^3 X^3+X^2 X+1  X X^2+X+1  1  1 X^2+X+1  1 X^3+X X+1  X  0 X^3+X^2+1 X^2  1  0
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3 X^2 X^2  0  0  0  0 X^2 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^2

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+111x^36+796x^37+1206x^38+2372x^39+2197x^40+3386x^41+2167x^42+2056x^43+997x^44+714x^45+203x^46+116x^47+22x^48+30x^49+5x^50+2x^53+3x^54

The gray image is a linear code over GF(2) with n=328, k=14 and d=144.
This code was found by Heurico 1.16 in 5.42 seconds.