The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X
 0 2X  0  0  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X  0 2X
 0  0 2X  0  0  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0  0 2X  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X
 0  0  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0 2X  0  0  0  0 2X 2X  0  0 2X  0  0 2X 2X
 0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X 2X
 0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0  0
 0  0  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X

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

Homogenous weight enumerator: w(x)=1x^0+28x^34+54x^36+54x^38+768x^39+52x^40+38x^42+16x^44+2x^46+3x^48+6x^50+1x^52+1x^68

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 3.05 seconds.