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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+132x^68+98x^70+400x^72+458x^74+1050x^76+1236x^78+1521x^80+1236x^82+1008x^84+458x^86+334x^88+98x^90+98x^92+38x^96+16x^100+9x^104+1x^120

The gray image is a code over GF(2) with n=320, k=13 and d=136.
This code was found by Heurico 1.16 in 8.65 seconds.