The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  2  1  1  2  2  2  1  1  1  X X^2  1  X  1
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+X X+2 X^2+X+2  2  2  2 X^2 X^2+X+2  X  2 X^2+X+2  X  X X^2+2 X^2 X^2+X X^2+X X^2 X^2  0 X^2+X  2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X+2 X^2+X X^2+X  X X^2 X^2+X+2  X  0 X^2+2 X^2+2 X^2+X+2 X+2 X+2  X  X X^2+X X^2  2 X^2+X+2  X X^2+X X^2+X X^2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  0  0  2  2  0  2  0  0  2  0  0  0  2  2  0  2  2  0  2  2  0  0  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+67x^32+186x^33+309x^34+552x^35+526x^36+910x^37+534x^38+472x^39+272x^40+110x^41+63x^42+64x^43+14x^44+10x^45+5x^46+1x^54

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 0.187 seconds.