The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+113x^28+274x^30+666x^32+1138x^34+1922x^36+1836x^38+1300x^40+524x^42+309x^44+66x^46+31x^48+2x^50+8x^52+2x^56

The gray image is a code over GF(2) with n=148, k=13 and d=56.
This code was found by Heurico 1.16 in 2.56 seconds.