The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  0  1  X  1  1  1  1  2  2  1  1  1  1  0  0  0  0  0  1  X  2  1
 0  1  1  0 X+1  1  X X+3  1  3  1 X+2  2 X+3  1 X+1  1  0  X  3  X  1  1 X+3 X+2  1  3  1  1  X  0  X  X  0  1  0
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  X X+2  2  0 X+2  0  X  2  X X+2  X X+2  0  X  0  0  2 X+2  X  X  X  X  X  0
 0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  2  2  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  0  0
 0  0  0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  0  2  2  0  2  2  2  2  0  0  2  2  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  0  2  0  0  2  2  0  2  2  2  0  2
 0  0  0  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  0  0  2  2  0  0  2  2  2  0  0  0  2  0  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+28x^28+106x^29+172x^30+342x^31+442x^32+648x^33+869x^34+916x^35+1124x^36+1012x^37+832x^38+696x^39+406x^40+248x^41+162x^42+92x^43+40x^44+34x^45+12x^46+2x^47+7x^48+1x^50

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 1.71 seconds.