The generator matrix

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

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+28x^34+94x^36+64x^37+152x^38+384x^39+126x^40+64x^41+60x^42+34x^44+16x^46+1x^64

The gray image is a code over GF(2) with n=312, k=10 and d=136.
This code was found by Heurico 1.16 in 0.437 seconds.