The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+154x^31+1253x^32+4000x^33+8965x^34+17738x^35+30876x^36+42610x^37+49843x^38+43906x^39+31184x^40+18030x^41+8677x^42+3216x^43+1156x^44+376x^45+129x^46+8x^47+10x^48+6x^49+2x^50+2x^51+2x^53

The gray image is a code over GF(2) with n=304, k=18 and d=124.
This code was found by Heurico 1.16 in 268 seconds.