The generator matrix

 1  0  0  1  1  1 X+2 3X+2  1  1  0  1  1  2  1  1  1  1  0  1 3X 2X+2 2X 3X+2  1 3X+2  1  1  1  1  1  1  1  0  1  1  1  1
 0  1  0  0 2X+3 X+1  1 2X  0 2X+1  1 3X X+3  1 3X+2 2X+1 2X+3 X+2  1 X+1  1 3X+2  1  1 2X+2  1  X  1 2X+1 2X+1 3X+2 3X+2 2X+2  1  X  0 2X+3  X
 0  0  1 X+1 X+1  0 X+3  1 3X+2  X 2X+3  3  1  X 3X+3 2X 2X+1 X+2  0 3X+2  3  1 2X+1 3X+2  3 3X X+3 X+1  2 2X+1  2 2X 3X+3 3X  3  1 X+3  X
 0  0  0  2 2X+2 2X  2  2 2X+2  2 2X  0 2X  0 2X+2 2X  2  0 2X+2  2  0 2X  2 2X+2  2  0  0  0  2 2X 2X  2 2X  2  2  0 2X 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+80x^33+722x^34+1356x^35+1974x^36+2660x^37+2940x^38+2638x^39+2062x^40+1102x^41+527x^42+212x^43+62x^44+12x^45+26x^46+2x^47+5x^48+2x^49+1x^50

The gray image is a code over GF(2) with n=304, k=14 and d=132.
This code was found by Heurico 1.16 in 1.44 seconds.