The generator matrix

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

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+130x^33+234x^34+276x^35+625x^36+460x^37+712x^38+570x^39+444x^40+258x^41+225x^42+58x^43+45x^44+32x^45+10x^46+6x^47+5x^48+3x^50+2x^51

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 87.6 seconds.