The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1 X^2  1  1  1 X^2+2  1  X  1  1  1  0  1  X  X  1  0  1  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+2 X^2+X+2  X X^2+2  X  0 X^2+2  X X^2 X^2+X+2 X^2+2  2 X^2+X+2 X^2+X X^2+2  X  X  X X^2+X+2  X  X X^2  X  0
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2  X X^2  X X+2 X^2+X+2 X+2  X X^2+X  2  2  X X^2+X  2  X  X X^2 X^2+2 X^2+2 X^2+X X^2+2  0  X X^2  0
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0 X^2+2  0  2  2  0 X^2+2  0  0  0  2 X^2 X^2+2 X^2 X^2+2  2 X^2 X^2+2  2  2  0  2 X^2+2  0  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+47x^32+170x^33+331x^34+524x^35+670x^36+744x^37+678x^38+412x^39+221x^40+150x^41+67x^42+40x^43+26x^44+8x^45+4x^46+2x^48+1x^56

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 0.188 seconds.