The generator matrix

 1  0  0  1  1  1  2 X^2  1  1  0  1  1  0  X  1  1 X^2+X  1  1 X+2 X^2+X+2  1 X^2+X+2 X^2  1  1  1  1 X+2  1 X^2  2  1  1  1
 0  1  0  0 X^2+3 X^2+3  1  X  2 X^2+1  1  2 X^2+1  1  1  X X+1  1 X^2+X+2 X^2+X+3 X^2+X+2 X^2 X^2+X  1  1 X^2+X+3 X+1  1  X  1 X^2  1  1 X+3 X^2+X+3 X^2+2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X+2  3  3 X^2+3 X+2 X^2+X  X  X  2  1 X^2+X+1 X+3  1  1  1 X^2+X+3  1 X^2+1 X^2+X+2 X^2+2  2 X+1 X+1 X^2 X^2+X+3 X^2+X X^2+X+2 X^2+X
 0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  0  2  0  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+189x^32+804x^33+1086x^34+1340x^35+1594x^36+1318x^37+905x^38+554x^39+206x^40+118x^41+40x^42+26x^43+10x^44+1x^46

The gray image is a code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 0.312 seconds.