The generator matrix

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

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+245x^76+200x^78+199x^80+176x^82+170x^84+8x^86+5x^88+13x^92+1x^96+1x^104+4x^108+1x^112

The gray image is a code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.16 in 0.329 seconds.