The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  2  X  2  X  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
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1 X+2  3  1  1  1  1  2  X X+3  3  2  X  2  X  2  X  2  X  0 X+2  2  X  2  X  2  X X+3  3 X+3  3 X+3  1 X+3 X+3 X+1  1 X+3  3  0  1  1 X+1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  2  0  0  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  2  2

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+48x^77+30x^78+176x^79+62x^80+112x^81+32x^82+16x^83+32x^85+1x^94+1x^96+1x^126

The gray image is a code over GF(2) with n=320, k=9 and d=154.
This code was found by Heurico 1.16 in 63.8 seconds.