The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+9x^36+64x^37+109x^38+60x^39+6x^40+2x^41+3x^42+2x^53

The gray image is a code over GF(2) with n=304, k=8 and d=144.
This code was found by Heurico 1.16 in 0.015 seconds.