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

generates a code of length 82 over Z4[X]/(X^3+2,2X) 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 0.719 seconds.