The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+113x^34+128x^35+368x^36+560x^37+449x^38+928x^39+431x^40+560x^41+298x^42+128x^43+79x^44+33x^46+13x^48+3x^50+3x^52+1x^56

The gray image is a code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.25 seconds.