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

generates a code of length 38 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=304, k=12 and d=132.
This code was found by Heurico 1.16 in 88.7 seconds.