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

generates a code of length 39 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+56x^32+110x^36+96x^38+1536x^39+126x^40+32x^42+58x^44+25x^48+7x^52+1x^68

The gray image is a code over GF(2) with n=312, k=11 and d=128.
This code was found by Heurico 1.16 in 0.109 seconds.