The generator matrix

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

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+68x^77+107x^78+76x^79+82x^80+60x^81+18x^82+36x^83+41x^84+14x^85+3x^86+1x^88+1x^92+2x^101+1x^104+1x^112

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 0.36 seconds.