The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+357x^36+112x^37+552x^38+160x^39+450x^40+112x^41+184x^42+101x^44+16x^46+1x^48+1x^52+1x^60

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 91.8 seconds.