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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+129x^36+224x^38+256x^39+362x^40+51x^44+1x^72

The gray image is a code over GF(2) with n=312, k=10 and d=144.
This code was found by Heurico 1.16 in 17.6 seconds.