The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  0  1 X+2  1  1  0  1  X  0  0
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  0  3  1 X+2 X+1  1  0 X+1  1 X+2  3  0 X+1  1  0  1 X+2 X+1  1  3  0  1  1
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  2  2  2  0  0  2  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  0  0  2  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  2  0  0  2  2  0  2  2  2  0  0  2  2  0  2  2
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  0  0  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  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+116x^28+8x^29+156x^30+120x^31+647x^32+488x^33+988x^34+920x^35+1321x^36+920x^37+1012x^38+488x^39+605x^40+120x^41+148x^42+8x^43+98x^44+26x^48+1x^52+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 1.68 seconds.