The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+500x^32+1840x^33+4952x^34+9140x^35+16042x^36+20228x^37+24672x^38+21432x^39+16750x^40+8904x^41+4180x^42+1556x^43+634x^44+132x^45+96x^46+9x^48+4x^50

The gray image is a linear code over GF(2) with n=304, k=17 and d=128.
This code was found by Heurico 1.16 in 68.2 seconds.