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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+44x^66+6x^67+101x^68+72x^69+167x^70+176x^71+184x^72+346x^73+186x^74+684x^75+192x^76+1124x^77+162x^78+1328x^79+205x^80+1092x^81+206x^82+718x^83+171x^84+384x^85+144x^86+144x^87+96x^88+50x^89+75x^90+16x^91+42x^92+4x^93+22x^94+24x^96+13x^98+6x^100+1x^102+2x^104+3x^106+1x^114

The gray image is a code over GF(2) with n=316, k=13 and d=132.
This code was found by Heurico 1.16 in 8.55 seconds.