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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+59x^76+103x^78+16x^79+196x^80+368x^81+575x^82+368x^83+201x^84+16x^85+77x^86+47x^88+13x^90+7x^92+1x^156

The gray image is a code over GF(2) with n=656, k=11 and d=304.
This code was found by Heurico 1.16 in 0.718 seconds.