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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+132x^64+92x^66+906x^68+768x^70+28x^72+24x^74+52x^76+30x^80+12x^82+2x^84+1x^128

The gray image is a code over GF(2) with n=552, k=11 and d=256.
This code was found by Heurico 1.16 in 0.437 seconds.