The generator matrix

 1  0  1  1  1 X^2+X  1  1  2  1  1 X^2+X+2  1 X^2+2  1  1  X  1 X^2 X+2  1  1  1  1  1  1  0  0  1  1  X  1  1 X^2  1  1 X^2+X  1  1
 0  1 X+1 X^2+X X^2+1  1  3  2  1 X^2+X+1 X^2+X+2  1 X^2  1 X^2+3 X+2  1 X+1  1  1 X^2+2 X^2+X+3  X  1  0  0  1  1 X^2+3 X+1 X+2 X^2+X+3 X^2  1  X X^2+X+1  1  3 X^2+X+1
 0  0 X^2  0  2  0  2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2  0 X^2+2  2 X^2  0 X^2  2  0  2 X^2 X^2+2  0 X^2  0 X^2 X^2+2  2 X^2+2  0 X^2+2  2 X^2  2  0 X^2 X^2
 0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  0  2  2  2  0  0  2  2  0  0  2  0  2  0

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+240x^36+232x^37+504x^38+184x^39+450x^40+216x^41+152x^42+8x^43+50x^44+9x^48+2x^52

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.14 seconds.