The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+68x^36+160x^37+216x^38+256x^39+162x^40+64x^41+24x^42+40x^44+32x^45+1x^64

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 0.062 seconds.