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

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+101x^34+16x^35+126x^36+192x^37+427x^38+352x^39+421x^40+192x^41+93x^42+16x^43+85x^44+17x^46+5x^48+2x^50+1x^52+1x^64

The gray image is a code over GF(2) with n=312, k=11 and d=136.
This code was found by Heurico 1.16 in 1.37 seconds.