The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  X  1  1  1  0  1  0  X  0  1  X  X  0  1  1  X  X  X  X  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2 X+2  X  0 X+2 X+2 X+2  0 X+2  X  X  0  X X+2  X X+2 X+2  0  X  0 X+2  2 X+2 X+2  2  X
 0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  0  2  0  2  0  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  0  2  2  0  0  0  2  0  2  2  2  0  2  2  0  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2  0  2  2  0  0  0  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  0  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+190x^28+162x^30+641x^32+1104x^34+2065x^36+1828x^38+1322x^40+448x^42+317x^44+42x^46+66x^48+3x^52+2x^56+1x^60

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 34.4 seconds.