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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+167x^76+160x^79+369x^80+704x^81+256x^82+160x^83+166x^84+62x^88+2x^92+1x^156

The gray image is a code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 1.84 seconds.