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

generates a code of length 39 over Z4[X]/(X^3+2,2X) 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 0.266 seconds.