The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X X X X X X 1 X X 2 1 X X
0 X 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 2 X X X X X X X+2 X+2 X X+2 X+2 0 X X+2 0 2
0 0 X 0 0 0 0 0 0 0 X X+2 X X+2 X+2 X X+2 0 2 2 2 2 2 X X+2 0 0 X+2 X X+2 2 X+2 X X 2 X+2 X
0 0 0 X 0 0 0 X X+2 X X X 0 X+2 0 X+2 2 X 0 2 2 X X 0 0 0 2 X+2 2 0 X X X X X X+2 X+2
0 0 0 0 X 0 X X X 2 0 0 2 X+2 X X+2 X X X+2 X 2 X+2 0 0 0 X 0 X 2 X 2 X+2 0 0 X+2 X 2
0 0 0 0 0 X X 2 X+2 X+2 0 X X X 0 2 X 0 X+2 0 X X X 2 0 0 X 2 X X+2 2 X+2 2 X+2 X+2 0 X+2
0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 2 0 2 0 0 2 0 0 2 0 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+94x^28+234x^29+289x^30+424x^31+637x^32+900x^33+1192x^34+1486x^35+1825x^36+2120x^37+1924x^38+1468x^39+1282x^40+932x^41+610x^42+416x^43+231x^44+158x^45+75x^46+44x^47+24x^48+8x^49+6x^50+2x^51+1x^52+1x^60
The gray image is a code over GF(2) with n=148, k=14 and d=56.
This code was found by Heurico 1.16 in 9.26 seconds.