The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) 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 0.031 seconds.