The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+99x^32+316x^33+729x^34+616x^35+872x^36+416x^37+572x^38+248x^39+116x^40+36x^41+38x^42+32x^43+4x^46+1x^50

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 0.125 seconds.