The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^2+2  1 X+2  1  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1 X^2+2 X^2+X X^2+2  1  1  1  1 X+2  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3  3 X^2+2  1 X+2  1 X^2+1 X+1  0  1 X^2+X+3 X^2+X  1 X^2+1 X^2+X+3  3  0 X+2 X+2 X+1  1  1  1  3 X+1 X+3 X^2+2  1 X^2+2  0
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  2  2  2  0  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  0  2  2  2  0  0  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  2  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+41x^32+184x^33+234x^34+400x^35+360x^36+384x^37+208x^38+176x^39+44x^40+8x^41+4x^42+2x^48+2x^50

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.032 seconds.