The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+62x^33+122x^34+436x^35+298x^36+920x^37+475x^38+912x^39+253x^40+416x^41+101x^42+60x^43+21x^44+8x^45+5x^46+2x^48+2x^49+1x^50+1x^52

The gray image is a linear code over GF(2) with n=304, k=12 and d=132.
This code was found by Heurico 1.16 in 0.297 seconds.