The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+40x^33+76x^34+144x^35+64x^36+392x^37+616x^38+392x^39+59x^40+144x^41+76x^42+40x^43+3x^44+1x^68

The gray image is a code over GF(2) with n=304, k=11 and d=132.
This code was found by Heurico 1.16 in 0.093 seconds.