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

generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+128x^62+158x^64+264x^66+1024x^67+192x^68+184x^70+32x^72+56x^74+8x^78+1x^128

The gray image is a code over GF(2) with n=536, k=11 and d=248.
This code was found by Heurico 1.16 in 131 seconds.