The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+170x^31+1403x^32+3698x^33+9137x^34+17210x^35+31716x^36+42402x^37+49801x^38+43196x^39+32424x^40+17246x^41+8861x^42+3140x^43+1198x^44+390x^45+103x^46+26x^47+8x^48+8x^49+2x^50+2x^51+2x^52

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 290 seconds.