The generator matrix

 1  0  0  0  1  1  1  1 2X  1 3X+2  1  1 3X+2  2  1 2X  1  X  2 X+2  1 2X+2  1  X  1  X 2X  1  X 2X  1 3X 3X  1  X 2X  1
 0  1  0  0  0 2X  3 3X+1  1  3  1 X+1 X+2  2  1 3X 3X 3X+1 2X  1 X+2  2  1  0  1  1  X  1 2X+1  1 3X  3  1  1 3X 3X  1 3X+3
 0  0  1  0  1 3X+2  2 3X 3X+2  3  3 3X+3 X+1  1 X+1 2X  1 2X+3  2 2X  1 3X+3 X+3  0 X+2 X+3  1 3X 3X+1 2X  1 3X+2 3X+1  1 X+3 3X+2  X  X
 0  0  0  1  1 X+1 X+3 2X  1  0 2X+1 2X+1  2 3X+3 2X+2  X X+2  0  1 3X+2 3X+1 2X+3 3X+1 3X+1 2X+1  1 X+2 X+3 2X+2 2X 3X+1  2 X+2 X+1 X+3  1  X X+3
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X  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+481x^32+1846x^33+5237x^34+8496x^35+16234x^36+20688x^37+24599x^38+21052x^39+17212x^40+8336x^41+4389x^42+1608x^43+674x^44+168x^45+29x^46+12x^47+6x^48+2x^49+2x^50

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 72.5 seconds.