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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+116x^70+24x^71+343x^72+264x^73+606x^74+600x^75+791x^76+976x^77+1078x^78+1432x^79+1226x^80+1592x^81+1229x^82+1432x^83+1068x^84+1032x^85+741x^86+560x^87+486x^88+224x^89+258x^90+48x^91+135x^92+8x^93+53x^94+29x^96+9x^98+14x^100+3x^102+3x^104+2x^106+1x^110

The gray image is a code over GF(2) with n=324, k=14 and d=140.
This code was found by Heurico 1.16 in 65.3 seconds.