The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 2X+2  1  1 X+2  1  X  X  1  1  1  1  1 3X  1  1  0  1  0  1
 0  1 X+1 X+2  3  1 3X+3 2X+2  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 X+2  3  1 3X  0 2X+2 3X+2 2X+2  2 3X 2X+1  1 2X+2 X+1  1 3X+3  1  0
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X  0  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0 2X  0  0  0  0  0 2X 2X 2X  0  0 2X

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+48x^35+194x^36+304x^37+272x^38+400x^39+341x^40+272x^41+124x^42+64x^43+20x^44+4x^46+1x^48+2x^52+1x^56

The gray image is a code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 0.062 seconds.