The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  1  X  1  X  1  1  1  1  0  1  1 X+2  2  1 X+2  1  1 X+2  1  2  1 X+2  1  1  1  2  1  X  1  1  1  1  0  1 X+2  1  1  X  1  2  2  1  0  1  2  X  1  X  1  1  1  1  1  2  1  1  2  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1  X  1  1  X  3  1 X+1  1  1  X  3  0  1  2  3  1  1 X+2  1  0  1  1 X+2  1 X+1  1 X+1 X+1 X+2  1  2  1  X X+2 X+3 X+3  1 X+2  1 X+3  2  0  3  1  1 X+2  1  2  1 X+2  1 X+2  X X+1 X+1  0 X+1  X X+3  3  0  0
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X  X  0  2  2  X  X  2  X X+2  X  2  2  X  0  2 X+2  2 X+2  2  0 X+2  0 X+2  0  2  0  0  0  X X+2  0  X  X X+2  0  2  2 X+2  0  X X+2  X  2  0 X+2  X  X  X  X  2 X+2  X X+2 X+2  X X+2  X  2  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0  2  2  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  2  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  0  2  2  0  2  0  2  2  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  0  0  2  2  2  2  2  0  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  2  0  2  2  2  2  0  0  2  2  2  0  2  2  0  0  0  0  2  2  0  2  2  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  2  0  2  2  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  2  0  2  0  0  0  2  2  2  0  0  2  2  2  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0  0  0

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+37x^68+86x^69+150x^70+202x^71+371x^72+446x^73+567x^74+830x^75+1038x^76+1146x^77+1284x^78+1392x^79+1367x^80+1394x^81+1327x^82+1196x^83+943x^84+818x^85+592x^86+378x^87+275x^88+170x^89+129x^90+86x^91+41x^92+30x^93+32x^94+12x^95+16x^96+6x^97+9x^98+4x^100+6x^102+2x^104+1x^108

The gray image is a code over GF(2) with n=320, k=14 and d=136.
This code was found by Heurico 1.16 in 19.9 seconds.