The generator matrix

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

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+119x^32+148x^33+380x^34+516x^35+451x^36+984x^37+400x^38+504x^39+286x^40+148x^41+92x^42+4x^43+36x^44+24x^46+2x^48+1x^52

The gray image is a code over GF(2) with n=296, k=12 and d=128.
This code was found by Heurico 1.16 in 0.297 seconds.