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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+146x^68+2x^70+334x^72+90x^74+570x^76+624x^78+1543x^80+1652x^82+1569x^84+610x^86+499x^88+82x^90+248x^92+12x^94+136x^96+53x^100+15x^104+5x^108+1x^124

The gray image is a code over GF(2) with n=328, k=13 and d=136.
This code was found by Heurico 1.16 in 10.8 seconds.