The generator matrix

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

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+335x^32+16x^33+688x^34+528x^35+1113x^36+432x^37+616x^38+48x^39+227x^40+72x^42+18x^44+1x^48+1x^60

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 14.8 seconds.