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  2  1  X  X  1  2  X  1  X  0  0  1  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  0  X X+2  2 X+2  0  2  X  0  0  2 X+2 X+2  2 X+2  X  X  2 X+2  X  2  0  2
 0  0  X  0  0  0  X X+2  X  2  X X+2  0 X+2  0 X+2 X+2  X  2  X  2 X+2  X  X  X  0  2 X+2 X+2 X+2  X X+2  0  2 X+2  X
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  X X+2  2  2  X  2  2  2  0 X+2  0  X  2 X+2 X+2  0  0  X X+2  2  X  0  X
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2  2  0 X+2  0 X+2  0  X X+2 X+2 X+2 X+2  2  0  0  2  2  2  0  X  2  0 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2  0  0  2
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  0  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+135x^28+428x^30+32x^31+662x^32+288x^33+1100x^34+704x^35+1488x^36+704x^37+1160x^38+288x^39+677x^40+32x^41+284x^42+161x^44+36x^46+11x^48+1x^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 2.42 seconds.