The generator matrix

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

generates a code of length 37 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+402x^32+1170x^33+2572x^34+3896x^35+5452x^36+5780x^37+5731x^38+3946x^39+2203x^40+970x^41+442x^42+92x^43+86x^44+16x^45+7x^46+2x^47

The gray image is a code over GF(2) with n=296, k=15 and d=128.
This code was found by Heurico 1.16 in 8.41 seconds.