The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+186x^28+686x^29+1305x^30+2508x^31+3528x^32+5344x^33+6702x^34+8056x^35+8111x^36+8776x^37+7070x^38+5518x^39+3519x^40+2242x^41+1014x^42+548x^43+263x^44+102x^45+37x^46+10x^47+8x^48+2x^49

The gray image is a code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.13 in 27.6 seconds.