The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+158x^32+1094x^33+2527x^34+5160x^35+7540x^36+10908x^37+10733x^38+11122x^39+7573x^40+5142x^41+2237x^42+878x^43+310x^44+120x^45+15x^46+6x^47+10x^48+2x^51

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 19.5 seconds.