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

generates a code of length 38 over Z4[X]/(X^2+2) 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 86.1 seconds.