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  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  2  2  2  2  2  2  0  2  0  2  2  2  2  0  2  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  0  0  2
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  2  2  2  2  0  2  2  0  0  2  2  0  0  0  0  0  0  2  2  2  0  0  0  0  2  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  2  0  2  0  2  2  0  0  2  0  0  2  0  0  2  2  0  0  0  0  0  0  0  2  2  2  0  0  2

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+45x^76+32x^78+361x^80+32x^82+34x^84+6x^88+1x^156

The gray image is a code over GF(2) with n=320, k=9 and d=152.
This code was found by Heurico 1.16 in 0.508 seconds.