The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+214x^32+792x^33+1066x^34+1358x^35+1541x^36+1348x^37+860x^38+640x^39+214x^40+68x^41+66x^42+18x^43+5x^44+1x^48

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.