The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  0  1  1 X+2  2  1  1  1  1  X  1  1  0  1  1 X+2  0  1  1  1  1 X+2  1  1  0  1  1 X+2  2  1  1  1  1  X  X  X  X  X  1  X  0  1  1  0  2 X+2  2  0  1  1  X  X  1  1  1  X  2  X  1  1  1  1  0  X  2  X
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  1  3 X+1  0  1 X+2  3  1  1  2 X+3  X  3  1  0 X+1  1 X+2  3  1  1  0 X+1 X+2  3  1  0 X+1  1 X+2  3  1  1  2 X+3  X  1  1  0  2 X+2  X X+1  X  X X+1  3  X  1  1  1  X  1  1  X  1  3  1  1  0  X  2  1 X+3  3 X+3  1  1  1  1
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2
 0  0  0  0  2  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  0  2  0  2  0  2  0  0  2  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  0  2  2  2  2  0  2  0  2  2  2  0  0  0  2  0  2  0  2  2  0  0  0  0  2  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  0  0  0  0  2  2  2  0  2  0  2  0  2  2  2  2  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  0  2  2  0  2  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+316x^76+80x^78+315x^80+32x^82+214x^84+16x^86+43x^88+5x^92+1x^104+1x^140

The gray image is a code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.16 in 68.8 seconds.