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

generates a code of length 49 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+34x^42+65x^44+79x^46+100x^48+1536x^49+89x^50+60x^52+36x^54+18x^56+10x^58+9x^60+5x^62+1x^64+3x^66+1x^68+1x^84

The gray image is a code over GF(2) with n=392, k=11 and d=168.
This code was found by Heurico 1.16 in 81.2 seconds.