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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+40x^70+48x^71+134x^72+128x^73+227x^74+262x^75+324x^76+436x^77+497x^78+548x^79+588x^80+668x^81+594x^82+632x^83+579x^84+540x^85+432x^86+388x^87+281x^88+236x^89+178x^90+130x^91+94x^92+32x^93+50x^94+40x^95+29x^96+8x^97+22x^98+11x^100+4x^102+7x^104+3x^106+1x^110

The gray image is a code over GF(2) with n=328, k=13 and d=140.
This code was found by Heurico 1.16 in 8.15 seconds.