The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+82x^76+138x^77+168x^78+440x^79+455x^80+782x^81+546x^82+1342x^83+875x^84+1588x^85+945x^86+1826x^87+1021x^88+1508x^89+888x^90+1314x^91+533x^92+694x^93+308x^94+388x^95+182x^96+122x^97+62x^98+42x^99+44x^100+28x^101+19x^102+18x^103+5x^104+4x^105+6x^106+6x^107+1x^108+2x^114+1x^116

The gray image is a code over GF(2) with n=348, k=14 and d=152.
This code was found by Heurico 1.16 in 21.8 seconds.