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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+72x^68+20x^69+67x^70+42x^71+149x^72+96x^73+263x^74+210x^75+526x^76+236x^77+845x^78+260x^79+1198x^80+320x^81+1196x^82+260x^83+820x^84+236x^85+496x^86+210x^87+214x^88+96x^89+113x^90+42x^91+62x^92+20x^93+52x^94+17x^96+26x^98+8x^100+11x^102+5x^104+2x^106+1x^126

The gray image is a code over GF(2) with n=324, k=13 and d=136.
This code was found by Heurico 1.16 in 8.55 seconds.