The generator matrix

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

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+134x^76+140x^77+208x^78+124x^79+110x^80+28x^81+46x^82+28x^83+35x^84+24x^85+52x^86+36x^87+45x^88+2x^90+1x^92+4x^94+4x^95+1x^96+1x^104

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 0.31 seconds.