The generator matrix

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

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+91x^32+160x^33+67x^34+384x^35+1024x^36+128x^39+36x^40+96x^41+60x^42+1x^66

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 0.078 seconds.