The generator matrix

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

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+210x^28+350x^30+951x^32+1544x^34+2081x^36+1572x^38+931x^40+360x^42+156x^44+14x^46+18x^48+1x^52+3x^56

The gray image is a code over GF(2) with n=144, k=13 and d=56.
This code was found by Heurico 1.16 in 4.49 seconds.