The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X X 1 X 1
0 X 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 2 0 2 2 X X X X+2 X+2 X X+2 X X+2 X+2 X+2 X+2 X X 0 0 0 X X X+2 2 0 X 0 X+2 0 0
0 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X 0 2 2 0 X+2 X+2 X+2 X 2 0 X 2 0 X X+2 2 0 2 X 2 X X X+2 X+2 2 X 0 X X+2 X 0 0
0 0 0 X 0 0 0 X X+2 X X X 0 X 2 X 0 0 X+2 2 2 2 X+2 X X X 2 X+2 2 X 0 0 0 2 2 0 0 2 0 X 0 0 X X+2 0 X X+2 0 0
0 0 0 0 X 0 X X X 2 X 2 X X+2 2 2 X+2 X X+2 X 2 2 2 0 X+2 X+2 0 X X+2 X 0 0 X 2 X 2 2 2 X+2 2 X X+2 2 X X+2 2 2 X 0
0 0 0 0 0 X X 2 X+2 X+2 X 0 X 0 X X+2 0 X+2 X+2 0 0 2 2 X 0 0 0 2 0 X 2 X+2 X X X+2 X+2 X+2 X+2 X+2 X+2 X+2 X X+2 X X X+2 2 X+2 0
0 0 0 0 0 0 2 2 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 0 2 0 0 0 2 0 0 0 2 2 2 2 0 2 0 2 2 0 2 0 0 2 0
generates a code of length 49 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+53x^38+76x^39+205x^40+262x^41+354x^42+360x^43+412x^44+592x^45+944x^46+1592x^47+2129x^48+2396x^49+2096x^50+1628x^51+992x^52+624x^53+436x^54+360x^55+303x^56+206x^57+198x^58+76x^59+52x^60+16x^61+14x^62+4x^63+2x^64+1x^86
The gray image is a code over GF(2) with n=196, k=14 and d=76.
This code was found by Heurico 1.16 in 13.7 seconds.