The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  2  1  2  0  1  1  X  X  X  1  1  1  X  1  2  X  1  1  0  1  1  1  1  0  2  1 X+2  1 X+2  0  0  1 X+2  1  2  1  0  X  X  1  1  X  1  2  1  1  1 X+2  1  1  1  1  1  1  2  1  1 X+2  X  1  1 X+2  0 X+2  1  2  0  X
 0  1  0  0  0  2  2  2  1 X+3 X+1 X+3  1 X+1  1  X  X X+2  1  0  1  3 X+1  1  1 X+2  0  1  0 X+2 X+2  2  3  0  1  1  1  3  1 X+1  0  1  1  2  1 X+1  1  3  X X+2  1 X+3 X+3  1  X  0  X X+1  3  X  X  3 X+1 X+3  0 X+3  1 X+2  2  1  1 X+3  3  0  X  1  X  1  X  1
 0  0  1  0  2  1  3  1 X+1  1  2  3 X+1  0  0  X  X X+2 X+2  1 X+3 X+3  X  2  1 X+1  1  2 X+1  0  1 X+3  1  X  X  1  2 X+3  3 X+1  1  2 X+1  3  0  3  3  3  1  X  0 X+1  X X+2  3  1  0 X+2  2  1 X+1 X+2 X+3  0 X+2 X+2 X+2  X X+3 X+2  X  2  1  1  1  0  2 X+1  0  2
 0  0  0  1 X+3 X+3  0 X+1  2  0  2 X+3  1 X+1  3  1  0  3  2  X  X  1 X+3  0 X+1  2  1  1  1  3  1  0  0  3  1  3 X+1 X+3 X+2  X  3  X X+3  1 X+1 X+2 X+2 X+3  X  1 X+2 X+1  2  X X+1  X X+3  2  3  3 X+1 X+2  0  3  0 X+2 X+3  X X+2 X+1  1  X  1  X X+1  X X+2 X+3  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+216x^74+312x^75+460x^76+364x^77+432x^78+376x^79+374x^80+244x^81+264x^82+188x^83+211x^84+132x^85+168x^86+84x^87+81x^88+52x^89+56x^90+20x^91+41x^92+8x^93+12x^95

The gray image is a code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.16 in 0.949 seconds.