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

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+45x^74+116x^76+48x^77+105x^78+256x^79+47x^80+128x^81+45x^82+64x^83+79x^84+16x^85+39x^86+12x^88+22x^90+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 0.443 seconds.