The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+198x^32+1034x^33+2795x^34+4516x^35+7991x^36+10660x^37+11099x^38+10810x^39+8354x^40+4218x^41+2343x^42+1072x^43+339x^44+56x^45+25x^46+18x^47+5x^48+2x^50

The gray image is a code over GF(2) with n=304, k=16 and d=128.
This code was found by Heurico 1.16 in 19.8 seconds.