The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  X  X  X  0  1  1  1  1  1  1  1  1  0  2  1  1
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  0  0  2 X+2  X  X  X  2  2  2  0  X  2 X+2  2  0  0  X  X  0
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2  X X+2  X  X  0  X  X  0  X  X  X X+2  X X+2  2  0  0  X X+2  2  2
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  0  2  2  0  2  2  0  2  0  2  0  0  2  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  0  0  2  2  0  0  0  0  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  0  0  2  2  0  2  2  0  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+30x^28+52x^29+108x^30+182x^31+208x^32+336x^33+416x^34+468x^35+562x^36+464x^37+400x^38+312x^39+178x^40+160x^41+80x^42+60x^43+38x^44+12x^45+20x^46+2x^47+5x^48+2x^52

The gray image is a code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.561 seconds.