The generator matrix

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

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+32x^74+56x^75+57x^76+84x^77+105x^78+132x^79+137x^80+120x^81+94x^82+66x^83+50x^84+28x^85+21x^86+16x^87+8x^88+8x^89+4x^90+2x^91+2x^92+1x^148

The gray image is a code over GF(2) with n=320, k=10 and d=148.
This code was found by Heurico 1.16 in 0.434 seconds.