The generator matrix

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

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+191x^32+252x^33+554x^34+656x^35+846x^36+632x^37+542x^38+240x^39+132x^40+12x^41+22x^42+8x^44+2x^46+4x^48+2x^52

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 0.14 seconds.