The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+100x^71+268x^72+430x^73+522x^74+646x^75+678x^76+614x^77+742x^78+692x^79+579x^80+580x^81+554x^82+478x^83+391x^84+324x^85+178x^86+136x^87+110x^88+62x^89+46x^90+18x^91+14x^92+6x^93+4x^94+8x^95+6x^96+2x^98+2x^99+1x^100

The gray image is a code over GF(2) with n=316, k=13 and d=142.
This code was found by Heurico 1.16 in 4.74 seconds.