The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+467x^32+2118x^33+4432x^34+9528x^35+15380x^36+21160x^37+24474x^38+21866x^39+15464x^40+9424x^41+4274x^42+1750x^43+492x^44+192x^45+30x^46+6x^47+4x^48+2x^49+6x^50+2x^51

The gray image is a code over GF(2) with n=304, k=17 and d=128.
This code was found by Heurico 1.16 in 73.4 seconds.