The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  X  1  0  1  1  2  1  1  0  2  1  1  1  0  0  0 X+2  X X+2  X X+2  X X+2  X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  2  1  X X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1  X  1  1  X X+1  X X+1  1  1  2  1  X  1 X+1  X  1  1  0  0 X+1  1  2 X+2  1  1  1  1  1  1  1  0  X X+1  X X+1  X  2  3  2  3 X+2 X+1  0 X+3  0  1  1  X  X  2  X X+3 X+2 X+2 X+3  X X+2 X+1 X+3 X+3  3  3 X+3 X+3  3  3  3 X+3 X+3 X+2  2  2  0
 0  0  1  1  2  3  1  1  X X+1  2  1  3  0  0 X+3  1 X+2 X+2  3 X+1 X+3  2 X+1 X+1  X  X  X  1  1  1  X X+1  1  0 X+3 X+2  1  0 X+2  1 X+3  1 X+3 X+2  0  3 X+3  3 X+2  2  1  2 X+3  1 X+2  1  1 X+1 X+2  0 X+3  2  X X+1 X+3  1 X+3 X+1  3  1 X+3  0  1  3  0 X+3  1  2 X+2
 0  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  2  0  0  2  0  0  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  2  0  0  0  0  2  0  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+131x^76+88x^77+272x^78+88x^79+109x^80+16x^81+112x^82+16x^83+59x^84+24x^85+40x^86+24x^87+24x^88+8x^90+9x^92+1x^96+1x^104+1x^108

The gray image is a code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.11 in 0.305 seconds.