The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+206x^74+318x^75+503x^76+276x^77+545x^78+282x^79+409x^80+226x^81+271x^82+142x^83+289x^84+128x^85+136x^86+86x^87+116x^88+42x^89+41x^90+20x^91+26x^92+16x^93+13x^94+4x^98

The gray image is a code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.11 in 0.538 seconds.