The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+25x^32+62x^34+32x^35+98x^36+64x^37+464x^38+576x^39+459x^40+64x^41+92x^42+32x^43+48x^44+16x^46+2x^48+6x^50+5x^52+1x^56+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 0.094 seconds.